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Medical imaging technologies are life-changing owing to their non-invasive approaches to early detection of diseases. X-ray Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are two routinely used imaging modalities. CT scans are typically performed in seconds yet can expose patients to X-ray ionizing radiation; MRI utilizing radiofrequency waves is free of ionizing radiation, yet, is notorious for its long scan times. Data undersampling is a common and practical approach to reducing ionizing radiation in CT and reducing scan times in MRI. While data undersampling eases the burden of data acquisition, it puts higher requirements on image reconstruction as the undersampling artifacts start to manifest. This dissertation exploits the emerging technique, deep learning, to tackle the problem of image reconstruction from undersampled data in both CT and MRI applications. This dissertation explores learned reconstruction in supervised and unsupervised settings. We first propose a fully supervised reconstruction method for sparse-view dedicated breast CT, leading to three times radiation dose reduction. Supervised learning typically requires a vast quantity of fully sampled data. To address this limitation, we propose a supervised reconstruction using accelerated reference as the training label for multiple MR parameter mapping applications. The accelerated references obtained from model based compressed sensing (CS) methods are slow yet accurate. By mapping to these accelerated references, the proposed learning method reduces the reconstruction times by several orders of magnitude in comparison to conventional CS methods, making them clinically relevant. Building off of these supervised learning methods, we propose a self-supervised learning framework that combines k-space view sharing techniques with image-space Noise2Noise denoising for highly accelerated radial MR parameter mapping. We show superior parameter accuracy than view sharing techniques and improv

Image segmentation is a partitioning of an image into distinct groups of pixels (“regions”), each region preferably spatially connected, where each region ideally corresponds to an object or other semantically meaningful scene component. In this dissertation we discuss supervised evaluation of segmentation algorithms and the common types of error. One major part of the supervised evaluation framework is the need for ground-truth segmentations. With the growing popularity of supervised deep-learning techniques for semantic segmentation, there are large sets of labeled data. When these ground-truth datasets have multiple ground-truth segmentations for each image, it is important to choose the most appropriate ground-truth segmentation or a fusion of these ground-truth segmentations for an unbiased evaluation of segmentation algorithms. We introduce a new hybrid ground-truth fusion method, and we provide qualitative and quantitative results to show that our new method performs better than existing methods. Superpixel segmentation is an image segmentation in which each region (“superpixel”) preferably forms a portion of an object or scene component rather than the whole, where each superpixel is preferably homogeneous with respect to certain features (e.g., color or texture). Superpixel segmentation algorithms facilitate subsequent image analysis by reducing the number of image primitives from the order of 105 – 107 pixels to a few hundreds of superpixels. Thereby, the computation time is greatly reduced for further post-processing steps such as region merging for image segmentation, object tracking, detection, depth estimation, object recognition, image denoising, object-based compression, video processing, video coding, saliency detection, and deep learning. We present a four-way experimental evaluation of the effectiveness of measures used to quantify the performance of superpixel algorithms. Choosing the right superpixel evaluation measure will significantly improve

We demonstrate the utility of task-based design and analysis methodology through its application to image compression and X-ray based threat detection system analysis. Two common tasks are considered for image compression: (1) perceptual image quality evaluation in the supra-threshold regime (i.e. with highly visible distortion) and (2) image classification. First, we propose and demonstrate a compression encoding method to optimize the perceptual image quality in supra-threshold regime for human observers. This approach is based on a distortion metric motivated by the HDR-VDP-2 image quality metric that emulates the human visual system’s perception of artifacts that arise in a compressed image. Whereas, most existing perceptual-optimized image compression methods aim to minimize the detectability of compression artifacts in the near-threshold regime, our proposed encoder aims to operate specifically in the supra-threshold regime where the human visual system’s perception of image quality can be quite different. We implement the proposed encoder within the JPEG 2000 image compression standard and demonstrate its advantage over both detectability-based and conventional mean square error (MSE) based encoders. Next, we present an image compression method for a machine/algorithm observer, i.e. an automated image exploitation algorithm. Traditional image compression methods primarily focus on maximizing the fidelity of the compressed image using image quality driven distortion metrics, which are ideally suited for human observers but are not necessarily optimal for machine observers. For machine observers, task-based distortion metrics, such as probability of error, have been shown to be more effective for tasks such as image classification. This motivates an approach to task-based image compression that preserves the relevant task-specific information (TSI). Our TSI-based encoder implementation is also JPEG 2000 compliant and thus inherits all its underlying scalability

Magnetic Resonance Imaging techniques such as Turbo Spin Echo (TSE) are routinely used in the clinic for the diagnosis of a variety of pathologies using tissue properties based on T2 relaxation for image contrast. Quantitative estimation of T2 relaxation using T2 maps can be used to further improve the quality of diagnosis in applications including cardiac, abdominal, neurological, and musculoskeletal imaging. A two-dimensional (2D) radial TSE (RADTSE) pulse sequence was previously proposed for T2-weighted imaging and T2 mapping. While RADTSE enables accelerated and accurate estimation of T2, it suffers from reduced slice coverage for breath-held abdominal imaging and black-blood myocardial imaging, leading to a compromise between slice coverage and scan time. Furthermore, the 2D nature of this pulse sequence makes it unsuitable for thin slice isotropic voxel imaging due to hardware limitations and signal to noise ratio (SNR) degradation. This dissertation is aimed at the design and development of novel techniques to improve the utility of RADTSE for clinical applications, providing efficient slice coverage within shorter scan times while maintaining T2 estimation accuracy and an acceptable SNR. A RADTSE pulse sequence with very long echo train lengths and variable refocusing flip angles is proposed to improve the slice coverage of 2D abdominal breath-held imaging. Accurate T2 estimation in the presence of imperfect slice profiles is enabled by introducing a partial volume corrected estimation algorithm. A multi-band excitation technique is presented to improve the slice and SNR efficiency of double inversion RADTSE for cardiac imaging. Finally, a radial stack-of-stars TSE pulse sequence is introduced for three dimensional (3D) isotropic T2-weighted imaging and T2 mapping for neurological and musculoskeletal applications. Performance of the proposed approaches are validated using numerical simulations, phantom experiments, and in vivo clinical data. The proposed tec

Tomographic imaging systems like CT and MRI allow the visualization of the interior of objects and are invaluable in diverse applications such as medical imaging and security scanning. These systems usually consist of two separate sub-systems: data acquisition and image reconstruction. Traditional imaging usually involves sampling at the Nyquist rate, and places the overwhelming burden of image formation on the data acquisition side. The reconstruction module simply acts as a mapping from the measurement space to image space. Acquiring data at the full sampling rate can be prohibitively expensive in several applications. There is tremendous interest in forming images from subsampled data to improve scanning throughput and reduce scan times. In diagnostic imaging, there are additional motivating factors to lower scan times: reduced patient discomfort, lowered motion sensitivity, and enabling novel imaging applications. Constrained imaging (CI) seeks to form images from subsampled data by enforcing suitable constraints on the images. A major difference from traditional imaging is that CI shifts a significant part of the image formation burden from the data acquisition system to the reconstruction system. MRI is a valuable tool for diagnostic applications but is popularly used as a qualitative imaging modality. However, MRI can also support the quantification of tissue specific parameters making it valuable for tissue characterization and pathological assessment. The mapping of tissue relaxation parameters like T1 and T2 is an emerging area of interest in quantitative MRI called parameter mapping. Classical parameter mapping experiments are plagued by extremely long scan times due to the need to form images with multiple contrast weightings. Using sub-sampled data for image formation is critical to allow these scans to be performed in a clinically acceptable time. This dissertation studies two different CI models for relaxation mapping. The proposed models seek to impr

Improving the efficiency of spectrum access and utilization under the umbrella of cognitive radio (CR) is one of the most crucial research areas for nearly two decades. The results have been algorithms called cognitive radio engines which use machine learning (ML) to learn and adapt the communication's link based on the operating scenarios. While a number of algorithms for cognitive engine design have been identified, it is widely understood that significant room remains to grow the capabilities of the cognitive engines, and substantially better spectrum utilization and higher throughput can be achieved if cognitive engines are improved. This requires working through some difficult challenges and takes an innovative look at the problem. A tenet of the existing cognitive engine designs is that they are usually designed around one primary ML algorithm or framework. In this dissertation, we discover that it is entirely possible for an algorithm to perform better in one operating scenario (combination of channel conditions, available energy, and operational objectives such as max throughput, and max energy efficiency) while performing less effectively in other operating scenarios. This arises due to the unique behavior of an individual ML algorithm regardless of its operating conditions. Therefore, there is no individual algorithm or parameter sets that have superiority in performance over all other algorithms or parameter sets in all operating scenarios. Using the same algorithm at all times may present a performance that is acceptable, yet may not be the best possible performance under all operating scenarios we are faced with over time. Ideally, the system should be able to adapt its behavior by switching between various ML algorithms or adjusting the operating ML algorithm for the prevailing operating conditions and goal. In this dissertation, we introduce a novel architecture for cognitive radio engines, with the goal of better cognitive engines for improved link a

In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where the occurrence probabilities are unknown for some of the symbols in an alphabet. Bounds can be obtained for alphabets of a given size, for alphabets of up to a given size, and for alphabets of arbitrary size. The method operates on a Computer Algebra System, yielding closed-form numbers for all results. Finally, we show the potential of the proposed method to shed some light on the structure of the minimum redundancy achievable by the Huffman code.

Compressive imaging exploits the inherent sparsity/compressibility of natural scenes to reduce the number of measurements required for reliable reconstruction/recovery. In many applications, however, additional scene prior information beyond sparsity (such as natural scene statistics) and task prior information may also be available. While current efforts on compressive measurement design attempt to exploit such scene and task priors in a heuristic/ad-hoc manner, in this dissertation, we develop a principled information-theoretic approach to this design problem that is able to fully exploit a probabilistic description (i.e. scene prior) of relevant scenes for a given task, along with the appropriate physical design constraints (e.g. photon count/exposure time) towards maximizing the system performance. We apply this information-theoretic framework to optimize compressive measurement designs, in EO/IR and X-ray spectral bands, for various detection/classification and estimation tasks. More specifically, we consider image reconstruction and target detection/classification tasks, and for each task we develop an information-optimal design framework for both static and adaptive measurements within parallel and sequential measurement architectures. For the image reconstruction task we show that the information-optimal static compressive measurement design is able to achieve significantly better compression ratios (and also reduced detector count, readout power/bandwidth) relative to various state-of-the-art compressive designs in the literature. Moreover, within a sequential measurement architecture our information-optimal adaptive design is able to successfully learn scene information online, i.e. from past measurement, and adapt next measurement (in a greedy sense) towards improving the measurement information efficiency, thereby providing additional performance gains beyond the corresponding static measurement design. We also develop a non-greedy adaptive measurement d

Traditionally the machine learning community has viewed the No Free Lunch (NFL) theorems for search and optimization as a limitation. I review, analyze, and unify the NFL theorem with the many frameworks to arrive at necessary conditions for improving black-box optimization, model selection, and machine learning in general. I review meta-learning literature to determine when and how meta-learning can benefit machine learning. We generalize meta-learning, in context of the NFL theorems, to arrive at a novel technique called Anti-Training with Sacrificial Data (ATSD). My technique applies at the meta level to arrive at domain specific algorithms and models. I also show how to generate sacrificial data. An extensive case study is presented along with simulated annealing results to demonstrate the efficacy of the ATSD method.

Stereoscopic 3-D has received considerable attention over the last few decades. Since a stereoscopic 3-D pair includes two 2-D images together, the amount of data for an uncompressed stereo image is double compared to that for an uncompressed 2-D image. Thus efficient compression techniques are of paramount importance. However, crosstalk effect is an inherent perceivable problem in current 3-D display technologies. It can lead not only to degradation in the perceived quality of 3-D images, but also to discomfort in some individuals. Correspondingly, when crosstalk occurs, the compression artifacts in a compressed stereo pair can be perceived, despite the fact that such artifacts are imperceptible in individual left and right images. This dissertation proposes a methodology for visually lossless compression of monochrome stereoscopic 3-D images in which crosstalk effect is carefully considered. In the proposed methodology for visually lossless compression of monochrome stereoscopic 3-D images, visibility thresholds are measured for quantization distortion in JPEG2000 to conceal perceivable compression artifacts. These thresholds are found to be functions of not only spatial frequency, but also of wavelet coefficient variance, as well as the gray level in both the left and right images. In order to avoid a daunting number of measurements of visibility thresholds during subjective experiments, a model for visibility thresholds is developed. The left image and right image of a stereo pair are then compressed jointly using the visibility thresholds obtained from the proposed model to ensure that quantization errors in each image are imperceptible to both eyes. This methodology is then demonstrated via a 3-D stereoscopic liquid crystal display (LCD) system with an associated viewing condition. The resulting images are visually lossless when displayed individually as 2-D images, and also when displayed in stereoscopic 3-D mode. In order to have better perceptual quality of

Magnetic recording systems have reached a point where the grain size can no longer be reduced due to energy stability constraints. As a new magnetic recording paradigm, two-dimensional magnetic recording (TDMR) relies on sophisticated signal processing and coding algorithms, a much less expensive alternative to radically altering the media or the read/write head as required for the other technologies. Due to 1) the significant reduction of grains per bit, and 2) the aggressive shingled writing, TDMR faces several formidable challenges. Firstly, severe interference is introduced in both down-track and cross-track directions due to the read/write head dimensions. Secondly, reduction in the number of grains per bit results in variations of bit boundaries which consequently lead to data-dependent jitter noise. Moreover, the bit to grain ratio reduction will cause some bits not to be properly magnetized or to be overwritten which introduces write errors to the system. The nature of write and read processes in TDMR necessitates that the information storage be viewed as a two-dimensional (2D) system. The challenges in TDMR signal processing are 1) an accurate read channel model, 2) mitigating the effect of inter-track interference (ITI) and inter-symbol interference (ISI) by using an equalizer, 3) developing 2D modulation/error correcting codes matching the TDMR channel model, 4) design of truly 2D detectors, and 5) computing the lower bounds on capacity of TDMR channel. The work is concerned with several objectives in regard to the challenges in TDMR systems. 1. TDMR Channel Modeling: As one of the challenges of the project, the 2D Microcell model is introduced as a read channel model for TDMR. This model captures the data-dependent properties of the media noise and it is well suited in regard to detector design. In line with what has been already done in TDMR channel models, improvements can be made to tune the 2D Microcell model for different bit to grain densities. Fur

The necessity for fast and efficient algorithms in different fields of communications and signal processing have led to developing low-complexity iterative algorithms. In the fields of compressed sensing and channel coding, which are the main focus of this dissertation, designing low-complexity iterative algorithms with excellent performance has been of interest for many years. Recently, there has been a significant interest to understanding the failures of the iterative reconstruction and decoding algorithms. Knowing the failures of the algorithms may improve the performance either by designing new algorithms or by providing new conditions on the input of the algorithms under which the previous failures of algorithms are disabled. In the first part of this dissertation, we consider an iterative reconstruction algorithm called the interval-passing algorithm (IPA) which was originally introduced to reconstruct non-negative signals from binary measurement matrices. We first modify the IPA to reconstruct signals from non-negative measurement matrices and compare the performance of the IPA with two reconstructing algorithms, the verification algorithm and the linear programming technique for recovery of signals. The results show that the IPA is a good trade-off between a very simple verification algorithm and the complex linear programming technique. We also show the failures of the IPA on some subgraphs in the Tanner graph corresponding to the measurement matrix called stopping sets and analyze the failures and successes of the IPA on subsets of stopping sets. We provide sufficient conditions under which the IPA succeeds the recovery of the signal. Reconstruction performance of the IPA using different LDPC measurement matrices is given to show the effect of stopping sets. In the second part of the dissertation, a method for constructing a class of codes called the check-hybrid generalized LDPC (CH-GLDPC) is provided. In CH-GLDPC codes, some single parity-checks are rep

Spread Spectrum (SS) techniques are methods used in communication systems where the spectra of the signal is spread over a much wider bandwidth. The large bandwidth of the resulting signals make SS signals difficult to intercept using conventional methods based on Nyquist sampling. Recently, a novel concept called compressive sensing has emerged. Compressive sensing theory suggests that a signal can be reconstructed from much fewer measurements than suggested by the Shannon Nyquist theorem, provided that the signal can be sparsely represented in a dictionary. In this work, motivated by this concept, we study compressive approaches to detect and decode SS signals. We propose compressive detection and decoding systems based both on random measurements (which have been the main focus of the CS literature) as well as designed measurement kernels that exploit prior knowledge of the SS signal. Compressive sensing methods for both Frequency-Hopping Spread Spectrum (FHSS) and Direct Sequence Spread Spectrum (DSSS) systems are proposed.

In this dissertation, applications of thermoacoustic (TA) effect in breast cancer detection and wireless communications are explored. Thermoacoustic imaging (TAI) is a promising candidate for breast cancer detection. TAI creates an image of the internal morphological features of a dielectrically lossy sample by employing generated acoustic waves from absorbed microwave energy in the sample owing to the thermoacoustic effect based on thermoelastic expansion. Malignant tissues, usually embracing higher dielectric loss, absorbing more energy and emanating stronger acoustic waves than the surrounding healthy tissues, may be distinguished in the image. Besides high contrast inherited from microwave imaging and excellent resolution inherited from ultrasound imaging, TAI is also non-ionizing and noninvasive compared with other existing breast cancer imaging modalities. A potential clinically feasible TAI system is more cost-efficient and compact than mammography and especially MRI. Two sets of breast model are investigated by simulations in this work. The first set is made of a slab-shaped breast model. The main purpose of this study is to perform safety evaluation of TAI and calculate the amount of microwave power needed to generate a detectable acoustic pressure. The second set employs four realistic numerical breast phantoms to study the feasibility of applying contrast agents to TAI for breast cancer imaging, which is named as contrast-enhanced TAI (CETAI). The presented results unveil the promising potential of CETAI as a complementary safe, rapid, sensitive, accurate, high-resolution and breast-density-insensitive tomography for 3-D breast cancer detection. Compressive sensing (CS) is applied to significantly reduce the required number of measurements and expedite CETAI applications in breast cancer detection. Results show that the total measurements can be reduced by at least a factor of 13, which is very favorable to potential clinical applications. The second appl

Iterative algorithms are now widely used in all areas of signal processing and digital communications. In modern communication systems, iterative algorithms are notably used for decoding low-density parity-check (LDPC) codes, a popular class of error-correction codes known to have exceptional error-rate performance under iterative decoding. In a more recent field known as compressed sensing, iterative algorithms are used as a method of reconstruction to recover a sparse signal from a linear set of measurements. This work primarily deals with the development of low-complexity iterative algorithms for the two aforementioned fields, namely, the design of low-complexity decoding algorithms for LDPC codes, and the development and analysis of a low complexity reconstruction algorithm for compressed sensing. In the first part of this dissertation, we focus on the decoding algorithms for LDPC codes. It is now well known that LDPC codes suffer from an error floor phenomenon in spite of their exceptional performance. This phenomenon originates from the failures of traditional iterative decoders, like belief propagation (BP), on certain low-noise configurations. Recently, a novel class of decoders, called finite alphabet iterative decoders (FAIDs), were proposed with the capability of surpassing BP in the error floor region at a much lower complexity. We show that numerous FAIDs can be designed, and among them only a few will have the ability of surpassing traditional decoders in the error floor region. In this work, we focus on the problem of the selection of good FAIDs for column-weight-three codes over the binary symmetric channel. Traditional methods for decoder selection use asymptotic techniques such as the density evolution method, but the designed decoders do not guarantee good performance for finite-length codes especially in the error floor region. Instead we propose a methodology to identify FAIDs with good error-rate performance in the error floor. This methodology

The recent renaissance of one particular class of error-correcting codes called low-density parity-check (LDPC) codes has revolutionized the area of communications leading to the so-called field of modern coding theory. At the heart of this theory lies the fact that LDPC codes can be efficiently decoded by an iterative inference algorithm known as belief propagation (BP) which operates on a graphical model of a code. With BP decoding, LDPC codes are able to achieve an exceptionally good error-rate performance as they can asymptotically approach Shannon's capacity. However, LDPC codes under BP decoding suffer from the error floor phenomenon, an abrupt degradation in the error-rate performance of the code in the high signal-to-noise ratio region, which prevents the decoder from achieving very low error-rates. It arises mainly due to the sub-optimality of BP decoding on finite-length loopy graphs. Moreover, the effects of finite precision that stem from hardware realizations of BP decoding can further worsen the error floor phenomenon. Over the past few years, the error floor problem has emerged as one of the most important problems in coding theory with applications now requiring very low error rates and faster processing speeds. Further, addressing the error floor problem while taking finite precision into account in the decoder design has remained a challenge. In this dissertation, we introduce a new paradigm for finite precision iterative decoding of LDPC codes over the binary symmetric channel (BSC). These novel decoders, referred to as finite alphabet iterative decoders (FAIDs), are capable of surpassing the BP in the error floor region at a much lower complexity and memory usage than BP without any compromise in decoding latency. The messages propagated by FAIDs are not quantized probabilities or log-likelihoods, and the variable node update functions do not mimic the BP decoder. Rather, the update functions are simple maps designed to ensure a higher guaranteed

This dissertation presents circuit techniques for designing high performance amplifiers. In low power design, the range of common mode input signal shrinks due to reduced power supply voltage. In addition, due to reduced bias current, noise density rises. The reduced input signal range and raised noise floor severely degrade system dynamic range. A novel rail to rail input circuit is presented. The proposed circuit has advantages over conventional circuits in term of noise and power consumption. Moreover, due to reduced bias current, low power amplifiers typically have lower bandwidth and slew rate, which limits their dynamic performance. The bandwidth is further reduced at high gain settings because of the constant gain bandwidth product. A novel self-adaptive compensation technique to extend small signal bandwidth and improve slew behavior is presented. If an amplifier needs to drive various capacitive and/or resistive loads, parallel Miller compensation is the most power efficient frequency compensation scheme. However, the frequency response of parallel Miller compensation is complicated and no thorough analysis on frequency response has been given in literatures. To illustrate the connection between poles/zeros and each individual circuit component, we use a design oriented approach to derive transfer functions for various load conditions. With these transfer functions, circuit designers can optimize their design accordingly. As a case study, a low power precision instrumentation amplifier is designed. Compared to low power instrumentation amplifiers on the market or reported in literature, it can save at least 40% power, meanwhile offer higher bandwidth and faster slew rate at typical gain settings. Many challenges also exist in designing high voltage amplifiers. To achieve low cost and high performance, a novel topology of a high voltage current sensing amplifier is proposed. With this topology, major portion of amplifiers can be designed with low voltage, fo

Generally speaking, a communication channel refers to a medium through which an information-bearing signal is corrupted by noise and distortion. A communication channel may result from data storage over time or data transmission through space. A primary task for communication engineers is to mathematically characterize the channel to facilitate the design of appropriate detection and coding systems. In this dissertation, two different channel modeling challenges for ultra-high density magnetic storage are investigated: two-dimensional magnetic recording (TDMR) and bit-patterned magnetic recording (BPMR). In the case of TDMR, we characterize the error mechanisms during the write/read process of data on a TDMR medium by a finite-state machine, and then design a state-based detector that provides soft decisions for use by an outer decoder. In the case of BPMR, we employ an insertion/deletion (I/D) model. We propose a LDPC-CRC product coding scheme that enables the error detection without the involvement of Marker codes specifically designed for an I/D channel. We also propose a generalized Gilbert-Elliott (GE) channel to approximate the I/D channel in the sense of an equivalent I/D event rate. A lower bound of the channel capacity for the BPMR channel is derived, which supports our claim that commonly used error-correction codes are effective on the I/D channel under the assumption that I/D events are limited to a finite length. Another channel model we investigated is perpendicular magnetic recording model. Advanced signal processing for the pattern-dependent-noise-predictive channel detectors is our focus. Specifically, we propose an adaptive scheme for a hardware design that reduces the complexity of the detector and the truncation/saturation error caused by a fix-point representation of values in the detector. Lastly, we designed a sequence detector for compressively sampled Bluetooth signals, thus allowing data recovery via sub-Nyquist sampling. This detector skip

[Abstract]: This paper sums up relevant topics covered by the special issue titled ‘Real-Time Multimedia Coding and Transmission’, including efficient content representation, multimedia transmission, hardware and software acceleration, and transcoding techniques.

Compressed sensing (CS) theory has demonstrated that sparse signals can be reconstructed from far fewer measurements than suggested by the Nyquist sampling theory. CS has received great attention recently as an alternative to the current paradigm of sampling followed by compression. Initial CS operated under the implicit assumption that the sparsity domain coefficients are independently distributed. Recent results, however, show that exploiting statistical dependencies in sparse signals improves the recovery performance of CS. This dissertation proposes model-based CS reconstruction techniques. Statistical dependency models for several CS problems are proposed and incorporated into different CS algorithms. These models allow incorporation of a priori information into the CS reconstruction problems. Firstly, we propose the use of a Bayes least squares-Gaussian scale mixtures (BLS-GSM) model for CS recovery of natural images. The BLS-GSM model is able to exploit dependencies inherent in wavelet coefficients. This model is incorporated into several recent CS algorithms. The resulting methods significantly reduce reconstruction errors and/or the number of measurements required to obtain a desired reconstruction quality, when compared to state-of-the-art model-based CS methods in the literature. The model-based CS reconstruction techniques are then extended to video. In addition to spatial dependencies, video sequences exhibit significant temporal dependencies as well. In this dissertation, a model for jointly exploiting spatial and temporal dependencies in video CS is also proposed. The proposed method enforces structural self-similarity of image blocks within each frame as well as across neighboring frames. By sparsely representing collections of similar blocks, dominant image structures are retained while noise and incoherent undersampling artifacts are eliminated. A new video CS algorithm which incorporates this model is then proposed. The proposed algorithm iterates

Error correcting codes are used in virtually all communication systems to ensure reliable transmission of information. In 1948, Shannon established an upper-bound on the maximum rate at which information can be transmitted reliably over a noisy channel. Reliably transmitting information with a rate close to this theoretical limit, known as the channel capacity, has been the goal of channel coding scientists for the last five decades. The rediscovery of low-density parity-check (LDPC) codes in the 1990s added much-renewed excitement in the coding community. LDPC codes are interesting because they can approach channel capacity under sub-optimum decoding algorithms whose complexity is linear in the code length. Unsurprisingly, LDPC codes quickly attained their popularity in practical applications such as magnetic storage, wireless and optical communications. One, if not the most, important and challenging problem in LDPC code research is the study and analysis of the error floor phenomenon. This phenomenon is described as an abrupt degradation in the frame error rate performance of LDPC codes in the high signal-to-noise ratio region. Error floor is harmful because its presence prevents the LDPC decoder from reaching very low probability of decoding failure, an important requirement for many applications. Not long after the rediscovery of LDPC codes, scientists established that error floor is caused by certain harmful structures, most commonly known as trapping sets, in the Tanner representation of a code. Since then, the study of error floor mostly consists of three major problems: 1) estimating error floor; 2) constructing LDPC codes with low error floor and 3) designing decoders that are less susceptible to error floor. Although some parts of this dissertation can be used as important elements in error floor estimation, our main contributions are a novel method for constructing LDPC codes with low error floor and a novel class of low complexity decoding algorithms th

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in parallel can offer low error floor decoding for high-speed applications. As the number of two-bit bit flipping algorithms is large, designing such a decoder is not a trivial task. In this paper, we describe a procedure to select collections of algorithms that work well together. This procedure relies on a recursive process which enumerates error configurations that are uncorrectable by a given algorithm. The error configurations uncorrectable by a given algorithm form its trapping set profile. Based on their trapping set profiles, algorithms are selected so that in parallel, they can correct a fixed number of errors with high probability., Comment: 5 pages, 1 figure, accepted for presentation at the IEEE International Symposium on Information Theory (ISIT) 2012

Image sizes have increased exponentially in recent years. The resulting high-resolution images are typically encoded in a lossy fashion to achieve high compression ratios. Lossy compression can be categorized into visually lossless and visually lossy compression depending on the visibility of compression artifacts. This dissertation proposes visually lossless coding methods as well as a visually lossy coding method with perceptual quality control. All resulting codestreams are JPEG2000 Part-I compliant.Visually lossless coding is increasingly considered as an alternative to numerically lossless coding. In order to hide compression artifacts caused by quantization, visibility thresholds (VTs) are measured and used for quantization of subbands in JPEG2000. In this work, VTs are experimentally determined from statistically modeled quantization distortion, which is based on the distribution of wavelet coefficients and the dead-zone quantizer of JPEG2000. The resulting VTs are adjusted for locally changing background through a visual masking model, and then used to determine the minimum number of coding passes to be included in a codestream for visually lossless quality under desired viewing conditions. The proposed coding scheme successfully yields visually lossless images at competitive bitrates compared to those of numerically lossless coding and visually lossless algorithms in the literature.This dissertation also investigates changes in VTs as a function of display resolution and proposes a method which effectively incorporates multiple VTs for various display resolutions into the JPEG2000 framework. The proposed coding method allows for visually lossless decoding at resolutions natively supported by the wavelet transform as well as arbitrary intermediate resolutions, using only a fraction of the full-resolution codestream. When images are browsed remotely, this method can significantly reduce bandwidth usage.Contrary to images encoded in the visually lossless manne

In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the min-sum algorithm at much lower complexity. Concatenation of two-bit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity., Comment: 6 pages. Submitted to IEEE International Symposium on Information Theory 2011

We are now in a rapid growth digital age. Different kinds of digitized applications are affecting people's daily life in different ways. All of these digitized applications generate tremendous amounts of information every day. We need to archive the important information because of their enduring value. However, the storage of digital information over time is a complex and difficult task. Selecting reliable digital archiving media, choosing suitable digital archiving methods, and using appropriate file formats for digital archiving are essential elements for achieving this task.Many companies and organizations have invested in finding reliable and affordable storage media for digital archiving since the end of the last century. Compact Disc Recordable (CD-R) quickly became one of the most popular choices for preserving digital information because CD-R can provide reliable back up at a reasonable price. Nevertheless, recent studies revealed that CD-R as a recording media for long term information archiving is not as reliable as we wish [4]. Its recording media may suffer from lost data because of possible damage from heat, humidity and light.In order to improve the performance of CD-R for long term digital archiving, there has been some research on hardware and software solutions to address this potential problem. Still most existing improvements have limitations either in the need of changing current CD-R standards or significant changes in current optical media drives.The objective of this research is to design and implement a novel system that advances the state of the art in digital archiving using CD-R, especially in the area of digital image storage. The design proposes robust image storage methods for CD-Rs based on the JPEG2000 standard. These storage methods combine the virtual block interleaver, Reed Solomon codes, and the error resilience tools of JPEG2000 effectively to protect the images on CD-Rs against errors caused by possible physical damage.To demon

This paper is concerned with the construction of low-density parity-check (LDPC) codes with low error floors. Two main contributions are made. First, a new class of structured LDPC codes is introduced. The parity check matrices of these codes are arrays of permutation matrices which are obtained from Latin squares and form a finite field under some matrix operations. Second, a method to construct LDPC codes with low error floors on the binary symmetric channel (BSC) is presented. Codes are constructed so that their Tanner graphs are free of certain small trapping sets. These trapping sets are selected from the Trapping Set Ontology for the Gallager A/B decoder. They are selected based on their relative harmfulness for a given decoding algorithm. We evaluate the relative harmfulness of different trapping sets for the sum product algorithm (SPA) by using the topological relations among them and by analyzing the decoding failures on one trapping set in the presence or absence of other trapping sets., Comment: This is a 21 page paper. It contains 18 figures and 4 tables. This paper was submitted to IEEE Transactions on Information Theory

The hard-disk storage industry is at a critical time as the current technologies are incapable of achieving densities beyond 500 Gb/in2, which will be reached in a few years. Many radically new storage architectures have been proposed, which along with advanced signal processing algorithms are expected to achieve much higher densities. In this dissertation, various signal processing algorithms are developed to improve the performance of current and next-generation magnetic storage systems.Low-density parity-check (LDPC) error correction codes are known to provide excellent performance in magnetic storage systems and are likely to replace or supplement currently used algebraic codes. Two methods are described to improve their performance in such systems. In the first method, the detector is modified to incorporate auxiliary LDPC parity checks. Using graph theoretical algorithms, a method to incorporate maximum number of such checks for a given complexity is provided. In the second method, a joint detection and decoding algorithm is developed that, unlike all other schemes, operates on the non-binary channel output symbols rather than input bits. Though sub-optimal, it is shown to provide the best known decoding performance for channels with memory more than 1, which are practically the most important.This dissertation also proposes a ternary magnetic recording system from a signal processing perspective. The advantage of this novel scheme is that it is capable of making magnetic transitions with two different but predetermined gradients. By developing optimal signal processing components like receivers, equalizers and detectors for this channel, the equivalence of this system to a two-track/two-head system is determined and its performance is analyzed. Consequently, it is shown that it is preferable to store information using this system, than to store using a binary system with inter-track interference. Finally, this dissertation provides a number of insights into t

With advances in imaging and communication systems, there is increased use of multi-dimensional images. Examples include multi-view image/video, hyperspectral image/video and dynamic volume imaging in CT/MRI/Ultrasound. These datasets consume even larger amounts of resources for transmission or storage compared to 2-D images. Hence, it is vital to have efficient compression methods for multi-dimensional images. In this dissertation, first, a JPEG2000 Part-2 compliant scheme is proposed for compressing multi-dimensional datasets for any dimension N>=3. Secondly, a novel view-compensated compression method is investigated for remote visualization of volumetric data. Experimental results indicate superior compression performance compared to state-of-the-art compression standards. Thirdly, a new scalable low complexity coder is designed that sacrifices some compression efficiency to get substantial gain in throughput. Potential use of the scalable low complexity coder is illustrated for two applications: Airborne video transmission and remote volume visualization.

This dissertation deals with techniques that enhance the detection of ground targets by airborne radar. The methods employed deal with the problem of air to ground detection by breaking the problem into two broad categories. The first category deals with improving detection of moving targets by using space-time adaptive processing (STAP) in a multistatic configuration. Mult-static STAP provides increased detection performance by observing targets from multiple perspectives. Multiple viewing perspectives afford more opportunities to the combined system for observing radial velocity of the target more directly, thus increasing Doppler that helps distinguish the target from background clutter. Detection performance also improves through an increased number of independent observations of a target, which reduces the likelihood of the target fading for the combined system. Increasing detection performance by increasing the number of independent observations is referred to in communications theory as channel diversity. The second part of this dissertation deals with the problem of distinguishing stationary targets from background clutter within a Synthetic Aperture Radar image. Stationary target discrimination is accomplished by exploiting the statistical nature of multifaceted metallic objects within a scene. The performance improvement for both moving and non-moving improvement methods is characterized and compared to other systems that attempt to accomplish the same end using different means.

Multiframe image superresolution has been an active research area for many years. In this approach image processing techniques are used to combine multiple low-resolution (LR) images capturing different views of an object. These multiple images are generally under-sampled, degraded by optical and pixel blurs, and corrupted by measurement noise. We exploit diversities in the imaging channels, namely, the number of cameras, magnification, position, and rotation, to undo degradations. Using an iterative back-projection (IBP) algorithm we quantify the improvements in image fidelity gained by using multiple frames compared to single frame, and discuss effects of system parameters on the reconstruction fidelity. As an example, for a system in which the pixel size is matched to optical blur size at a moderate detector noise, we can reduce the reconstruction root-mean-square-error by 570% by using 16 cameras and a large amount of diversity in deployment.We develop a new technique for superresolving binary imagery by incorporating finite-alphabet prior knowledge. We employ a message-passing based algorithm called two-dimensional distributed data detection (2D4) to estimate the object pixel likelihoods. We present a novel complexity-reduction technique that makes the algorithm suitable even for channels with support size as large as 5x5 object pixels. We compare the performance and complexity of 2D4 with that of IBP. In an imaging system with an optical blur spot matched to pixel size, and four 2x2 undersampled LR images, the reconstruction error for 2D4 is 300 times smaller than that for IBP at a signal-to-noise ratio of 38dB.We also present a transform-domain superresolution algorithm to efficiently incorporate sparsity as a form of prior knowledge. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular L1 norm as the regularization operator. Secondly we model wavelet coefficients of natural objects using generaliz

The traditional approach to imaging system design places the sole burden of image formation on optical components. In contrast, a computational imaging system relies on a combination of optics and post-processing to produce the final image and/or output measurement. Therefore, the joint-optimization (JO) of the optical and the post-processing degrees of freedom plays a critical role in the design of computational imaging systems. The JO framework also allows us to incorporate task-specific performance measures to optimize an imaging system for a specific task. In this dissertation, we consider the design of computational imaging systems within a JO framework for two separate tasks: object reconstruction and iris-recognition. The goal of these design studies is to optimize the imaging system to overcome the performance degradations introduced by under-sampled image measurements. Within the JO framework, we engineer the optical point spread function (PSF) of the imager, representing the optical degrees of freedom, in conjunction with the post-processing algorithm parameters to maximize the task performance. For the object reconstruction task, the optimized imaging system achieves a 50% improvement in resolution and nearly 20% lower reconstruction root-mean-square-error (RMSE ) as compared to the un-optimized imaging system. For the iris-recognition task, the optimized imaging system achieves a 33% improvement in false rejection ratio (FRR) for a fixed alarm ratio (FAR) relative to the conventional imaging system. The effect of the performance measures like resolution, RMSE, FRR, and FAR on the optimal design highlights the crucial role of task-specific design metrics in the JO framework. We introduce a fundamental measure of task-specific performance known as task-specific information (TSI), an information-theoretic measure that quantifies the information content of an image measurement relevant to a specific task. A variety of source-models are derived to illustrate

Low-density parity check (LDPC) codes have experienced tremendous popularity due to their capacity-achieving performance. In this dissertation, several different aspects of LDPC coding and its applications to magnetic storage are investigated. One of the most significant issues that impedes the use of LDPC codes in many systems is the error-rate floor phenomenon associated with their iterative decoders. By delineating the fundamental principles, we extend to partial response channels algorithms for predicting the error rate performance in the floor region for the binary-input AWGN channel. We develop three classes of decoding algorithms for mitigating the error floor by directly tackling the cause of the problem: trapping sets. In our experiments, these algorithms provide multiple orders of improvement over conventional decoders at the cost of various implementation complexity increases.Product codes are widely used in magnetic recording systems where errors are both isolated and bursty. A dual-mode decoding technique for Reed-Solomon-code-based product codes is proposed, where the second decoding mode involves maximum-likelihood erasure decoding of the binary images of the Reed-Solomon codewords. By exploring a tape storage application, we demonstrate that this dual-mode decoding system dramatically improves the performance of product codes. Moreover, the complexity added by the second decoding mode is manageable. We also show the performance of this technique on a product code which has an LDPC code in the columns.Run-length-limited (RLL) codes are ubiquitous in today's disk drives. Using RLL codes has enabled drive designers to pack data very efficiently onto the platter surface by ensuring stable symbol-timing recovery. We consider a concatenation system design with an LDPC code and an RLL code as components to simultaneously achieve desirable features such as: soft information availability to the LDPC decoder, the preservation of the LDPC code's structure, and

Ever since the publication of Shannon's seminal work in 1948, the search for capacity achieving codes has led to many interesting discoveries in channel coding theory. Low-density parity-check (LDPC) codes originally proposed in 1963 were largely forgotten and rediscovered recently. The significance of LDPC codes lies in their capacity approaching performance even when decoded using low complexity sub-optimal decoding algorithms. Iterative decoders are one such class of decoders that work on a graphical representation of a code known as the Tanner graph. Their properties have been well understood in the asymptotic limit of the code length going to infinity. However, the behavior of various decoders for a given finite length code remains largely unknown.An understanding of the failures of the decoders is vital for the error floor analysis of a given code. Broadly speaking, error floor is the abrupt degradation in the frame error rate (FER) performance of a code in the high signal-to-noise ratio domain. Since the error floor phenomenon manifests in the regions not reachable by Monte-Carlo simulations, analytical methods are necessary for characterizing the decoding failures. In this work, we consider hard decision decoders for transmission over the binary symmetric channel (BSC).For column-weight-three codes, we provide tight upper and lower bounds on the guaranteed error correction capability of a code under the Gallager A algorithm by studying combinatorial objects known as trapping sets. For higher column weight codes, we establish bounds on the minimum number of variable nodes that achieve certain expansion as a function of the girth of the underlying Tanner graph, thereby obtaining lower bounds on the guaranteed error correction capability. We explore the relationship between a class of graphs known as cage graphs and trapping sets to establish upper bounds on the error correction capability.We also propose an algorithm to identify the most probable noise configu

In this paper, we give necessary and sufficient conditions for low-density parity-check (LDPC) codes with column-weight three to correct three errors when decoded using hard-decision message-passing decoding. Additionally, we give necessary and sufficient conditions for column-weight-four codes to correct three errors in four iterations of hard-decision message-passing decoding. We then give a construction technique which results in codes satisfying these conditions. We also provide numerical assessment of code performance via simulation results., Comment: 25 pages. 11 Figures. Part of the work was presented at the Information Theory Workshop (ITW), May 5-9 2008, Porto, Portugal. submitted to IEEE Transactions on Information Theory

The relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least $3 \gamma/4$ is found based on the Moore bound. An upper bound on the guaranteed error correction capability is established by studying the sizes of smallest possible trapping sets. The results are extended to generalized LDPC codes. It is shown that generalized LDPC codes can correct a linear fraction of errors under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. It is also shown that the bound cannot be improved when $\gamma$ is even by studying a class of trapping sets. A lower bound on the size of variable node sets which have the required expansion is established., Comment: 17 pages. Submitted to IEEE Transactions on Information Theory. Parts of this work have been accepted for presentation at the International Symposium on Information Theory (ISIT'08) and the International Telemetering Conference (ITC'08)

The relation between the girth and the error correction capability of column-weight-three LDPC codes is investigated. Specifically, it is shown that the Gallager A algorithm can correct $g/2-1$ errors in $g/2$ iterations on a Tanner graph of girth $g \geq 10$., Comment: 7 pages, 7 figures, submitted to IEEE Transactions on Information Theory (July 2008)

In today's world, demands of digital multimedia services are growing tremendously, together with the development of new communication technologies and investigation of new transmission media. Two common problems encountered in multimedia services are unreliable transmission channels and limited resources. This dissertation investigates advanced source coding and error control techniques, and is dedicated to designing joint source-channel coding schemes for robust image/video transmission. Error resilience properties of JPEG2000 codestreams are investigated first, and an LDPC-based joint iterative decoding scheme is proposed. Next, a progressive decoding method is presented for still and motion image transmission. The underlying channel codes are created using a Plotkin construction and offer the novel ability of using one long channel codeword to protect an entire image, yet still allowing progressive decoding. Progressive quality improvements occur in two ways: the first is the usual progressive refinement, where image quality is improved as more data are received; the second is that residual error rates of earlier received data are reduced as more data are received. Finally, multichannel systems are studied and an optimal rate allocation algorithm is proposed for parallel transmission of scalable images in multichannel systems. The proposed algorithm selects a subchannel as well as a channel code rate for each packet, based on the signal-to-noise ratios (SNR) of the subchannels. The resulting scheme provides unequal error protection of source bits and significant gains are obtained over equal error protection (EEP) schemes. An application of the proposed algorithm to JPEG2000 transmission shows the advantages of exploiting differences in SNRs between subchannels. Multiplexing of multiple sources is also considered, and additional gains are achieved by exploiting information diversity among the sources.

This dissertation presents four technical contributions in the theory and practice of low-density parity-check (LDPC) codes and orthogonal frequency division multiplexing (OFDM) systems withtransmission non-linearity and with interference due to high mobility.We first explore the universality of LDPC codes for the binary erasure channel (BEC), the AWGN channel, and the flat Rayleigh fading channel. Using excess mutual information as a performance measure, we demonstrate that an LDPC code designed on a singlechannel can be universally good across the three channels. Thus, a channel for which LDPC code design is simple may be used as a surrogate for channels that are more challenging.Due to fast channel variations, OFDM systems suffer from inter-carrier interference (ICI) in frequency-selective fast fading channels. We propose a novel iterative receiver design that achieves near-optimal performance while maintaining a complexity that grows only linearly with the number of OFDM carriers. Weprove that the matched filter bound for such a channel is also the maximum-likelihood sequence detection (MLSD) bound.Because of the presence of high peaks at OFDM modulator output, amplitude clipping due to amplifier saturation causes performance degradation. We show that existing analyses underestimate the capacity of OFDM systems with clipping, and we analyze thecapacity of clipped OFDM systems with AWGN and frequency-selective Rayleigh fading. We prove that for frequency-selective Rayleigh fading channels, under certain conditions, there exists an SNR threshold, above which the capacity of a clipped system is higherthan that of an unclipped system. We provide upper and lower bounds on the channel capacity and closed-form approximations of discrete-input capacities with and without clipping.We also derive tight MLSD lower bounds and propose near-optimal receivers for OFDM systems with clipping. We show that over frequency-selective Rayleigh fading channels, under certain condition

This dissertation describes the design and implementation of a computer vision based varve image analysis system. The primary issues covered are software engineering design, varve image calibrations, varve image enhancement, varve Dynamic Spatial Warping (DSW) profile generation, varve core image registration, varve identification, boundary identification and varve thickness measurement. A varve DSW matching algorithm is described to generate DSW profile and register two core images. Wavelet Multiple Resolution Analysis (MRA) is also used to do the core image registrations. By allowing an analyst to concentrate on other research work while the VARVES software analyzes a sample, much of the tedious varve analysis work is reduced, and potentially increasing the productivity. Additionally, by using new computer vision techniques, VARVES system is able to do some varve analysis which was impossible handled manually.

Functional electrical stimulation (FES) involves artificial activation of paralyzed muscles via implanted electrodes. FES has been successfully used to improve the ability of tetraplegics to perform upper limb movements important for daily activities. The variety of movements that can be generated by FES is, however, limited to a few movements such as hand grasp and release. Ideally, a user of an FES system would have effortless command over all of the degrees of freedom associated with upper limb movement. One reason that a broader range of movements has not been implemented is because of the substantial challenge associated with identifying the patterns of muscle stimulation needed to elicit additional movements. The first part of this dissertation addresses this challenge by using a probabilistic algorithm to estimate the patterns of muscle activity associated with a wide range of upper limb movements.A neuroprosthetic involves the control of an external device via brain activity. Neuroprosthetics have been successfully used to improve the ability of tetraplegics to perform tasks important for interfacing with the world around them. The variety of mechanisms which they can control is, however, limited to a few devices such as special computer typing programs. Because motor areas of the cerebral cortex are known to represent and regulate voluntary arm movements it might be possible to sense this activity with electrodes and decipher this information in terms of a moment-by-moment representation of arm trajectory. Indeed, several methods for decoding neural activity have been described, but these approaches are encumbered by technical difficulties. The second part of this dissertation addresses this challenge by using similar probabilistic methods to extract arm trajectory information from electroencephalography (EEG) electrodes that are already chronically deployed and widely used in human subjects.Ultimately, the two approaches developed as part of this dissertat

Problems at the intersection of compression and statistical inference recur frequently due to the concurrent use of signal and image compression and classification algorithms in many applications. This dissertation addresses two such problems: statistical inference on compressed data, and rate-allocation for joint compression and classification.Features of the JPEG2000 standard make possible the development of computationally efficient algorithms to achieve such a goal for imagery compressed using this standard. We propose the use of the information content (IC) of wavelet subbands, defined as the number of bytes that the JPEG2000 encoder spends to compress the subbands, for content analysis. Applying statistical learning frameworks for detection and classification, we present experimental results for compressed-domain texture image classification and cut detection in video. Our results indicate that reasonable performance can be achieved, while saving computational and bandwidth resources. IC features can also be used for preliminary analysis in the compressed domain to identify candidates for further analysis in the decompressed domain.In many applications of image compression, the compressed image is to be presented to human observers and statistical decision-making systems. In such applications, the fidelity criterion with respect to which the image is compressed must be selected to strike an appropriate compromise between the (possibly conflicting) image quality criteria for the human and machine observers. We present tractable distortion measures based on the Bhattacharyya distance (BD) and a new upper bound on the quantized probability of error that make possible closed form expressions for rate allocation to image subbands and show their efficacy in maintaining the aforementioned balance between compression and classification. The new bound offers two advantages over the BD in that it yields closed-form solutions for rate-allocation in problems involving cor

The growing popularity of a class of linear block codes called the low-density parity-check (LDPC) codes can be attributed to the low complexity of the iterative decoders, and their potential to achieve performance very close to the Shannon capacity. This makes them an attractive candidate for ECC applications in communication systems. This report proposes methods to systematically construct regular and irregular LDPC codes.A class of regular LDPC codes are constructed from incidence structures in finite geometries like projective geometry and affine geometry. A class of irregular LDPC codes are constructed by systematically splitting blocks of balanced incomplete block designs to achieve desired weight distributions. These codes are decoded iteratively using message-passing algorithms, and the performance of these codes for various channels are presented in this report.The application of iterative decoders is generally limited to a class of codes whose graph representations are free of small cycles. Unfortunately, the large class of conventional algebraic codes, like RS codes, has several four cycles in their graph representations. This report proposes an algorithm that aims to alleviate this drawback by constructing an equivalent graph representation that is free of four cycles. It is theoretically shown that the four-cycle free representation is better suited to iterative erasure decoding than the conventional representation. Also, the new representation is exploited to realize, with limited success, iterative decoding of Reed-Solomon codes over the additive white Gaussian noise channel.Wiberg, Forney, Richardson, Koetter, and Vontobel have made significant contributions in developing theoretical frameworks that facilitate finite length analysis of codes. With an exception of Richardson's, most of the other frameworks are much suited for the analysis of short codes. In this report, we further the understanding of the failures in iterative decoders for the binary

Body magnetic resonance imaging (MRI) has progressed rapidly over the last 12 years. The advances in hardware and software have allowed the implementation of faster and better pulse sequences for body imaging. Despite the improvements in MRI technology there are still problems associated with current body MRI techniques that limit their diagnostic capabilities. The main goal of this work is to develop novel body MRI methods to improve the diagnosis of cardiac and abdominal pathologies. One of the goals of this work is to develop a technique to improve the detection of lipid infiltration in the heart. For this purpose an interleaved double-inversion fast spin-echo technique was developed. The method yields co-registered lipid and water images of the heart from data acquired in a single breath hold, producing data with optimal contrast between lipid and myocardium as well as minimal artifacts caused by chemical shift and blood flow.A technique combining GRAdient and Spin-Echo (GRASE) data acquisition and an iterative algorithm for lipid-water separation (Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation, IDEAL) was also developed. By shifting the typical GRASE data acquisition and employing correction for phase errors due to eddy currents, the IDEAL-GRASE technique achieves more time-efficient and robust lipid-water decomposition in the presence of field inhomogeneities. The technique was developed to acquire data for Cartesian and radial k-space trajectories. The radial IDEAL-GRASE with auto-correction of phase errors was developed to accomplish insensitivity to motion artifacts as well as for the generation of high resolution parametric maps (T2 and T2) for tissue characterization.A radial "variable flip angle" Steady-State Free Precession (SSFP) technique with slice profile correction was also developed to obtain fast estimation of another parameter, i.e. the T1/T2 value. This method was developed as an alternative for fast p

Distributed imaging using sensor arrays is gaining popularity among various research and development communities. A common bottleneck within such an imaging sensor network is the large resulting data load. In applications for which transmission power and/or bandwidth are constrained, this can drastically decrease the network lifetime. In this dissertation, we consider a network of imaging sensors. We address the problem of energy-efficient communication of the resulting measurements. First, we develop a heuristic-based method that exploits the redundancy in the measurements of imaging sensors. The algorithm attempts to maximize the lifetime of the network without utilizing inter-sensor communication. Gains in network lifetime up to 114% are obtained when using the suggested algorithm with lossless compression. Our results also demonstrate that when lossy compression is employed, much larger gains are achieved. For example, when a normalized Root-Mean-Squared- Error of 0.78% can be tolerated in the received measurements, the network lifetime increases by a factor of 2.8, as compared to the lossless case. Second, we develop a novel theory for maximizing the lifetime of unicast multihop wireless sensor networks. An optimal centralized solution is presented in the form of an iterative algorithm. The algorithm attempts to find a Pareto Optimal solution. In the first iteration, the minimum lifetime of the network is maximized. If the solution is not Pareto Optimal a second iteration is performed which maximizes the second minimum lifetime subject to the minimum lifetime being maximum. At the nth iteration, the algorithm maximizes the nth minimum lifetime subject to the (n−1)th minimum lifetime being maximum, subject to the (n−2)th minimum lifetime being maximum, etc. The algorithm can be stopped at any iteration n. Third, we present a novel algorithm for the purpose of exploiting the inherent inter- and intra-sensor correlation in a network of imaging sensors while utiliz

This dissertation provides a comprehensive analysis of the coding-spreading tradeoff problem in finite-sized synchronous DS-CDMA systems. In contrast to the large system which has a large number of users, the finite-sized system refers to a system with a small number of users. Much work has been performed in the past on the analysis of the spectral efficiency of synchronous DS-CDMA systems and the associated coding-spreading tradeoff problem. However, most of the analysis is based on the large-system assumptions. In this dissertation, we focused on finite-sized systems with the help of numerical methods and Monte-Carlo simulations.Binary-input achievable information rates for finite-sized synchronous DS-CDMA systems with different detection/decoding schemes on AWGN channel are numerically calculated for various coding/spreading apportionments. We use these results to determine the existence and value of an optimal code rate for a number of different multiuser receivers, where optimality is in the sense of minimizing the SNR required for reliable multiuser communication. Our results are consistent with the well-known fact that all coding (no spreading) is optimal for the maximum a posteriori receiver.Simulations of the LDPC-coded synchronous DS-CDMA systems with iterative multiuser detection/decoding and MMSE multiuser detection/single-user decoding are also presented to show that the binary-input capacities can be closely approached with practical schemes. The coding-spreading tradeoff is examined using these LDPC code simulation results, where agreement with the information-theoretic results is demonstrated.We extend our work to the DS-CDMA systems on two idealized Rayleigh flat-fading channels: the chip-level flat-fading (CLFF) and the (code) symbol-level flat-fading (SLFF). These models represent ideal fast fading and slow fading channels, respectively. Both information-theoretic results and LDPC code simulation results are presented to show the effects of channe

In this dissertation, I design a processing approach, implement and test several solutions to combining spatial and spectral processing of multisource data. The measured spectral information is assumed to come from a multispectral or hyperspectral imaging system with low spatial resolution. Thematic content from a higher spatial resolution sensor is used to spatially localize different materials by their spectral signature. This approach results in both spectralunmixing and sharpening, a spatial-spectral fusion. The main real imagery example, fusion of polarimetric synthetic aperture radar (SAR) with hyperspectral imagery, poses a unique challenge due to the phenomenological differences between the sensors.Theoretical models for electro-optical image formation and scene reflectivity are shown to lead naturally to a set of pixel mixing equations. Several solutions for the spatial unmixing form of these equations are examined, based on the method of least squares. In particular, a method for introducing thematic content into the solution for spatial unmixing is defined using weighted least squares. Finally, and most significantly, a spatial-spectral fusion algorithm based on the theory of projection onto convex sets (POCS) is presented. Theoretical aspects of POCS are briefly discussed, showing how the use of constraints in the form of closed convex sets drives the solution. Then, constraints are derived that are intimately tied to the underlying theoretical models. Simulated imagery is used to characterize the different constraintcombinations that can be used in a POCS-based fusion algorithm.The fusion algorithms are applied to real imagery from two data sets, a Landsat ETM+ scene over Tucson, AZ and an AVIRIS/AirSAR scene over Tombstone, AZ. The results of the fusion are analyzed using scattergrams and correlation statistics. The POCS-based fusion algorithm is shown to produce a reasonable fusion of the AVIRIS/AirSAR data, with some sharpening of spatial-spectral fe

For this work, two iterative methods were developed which combine a parametric channel model with the maximum likelihood and cross-correlation estimation techniques in order to estimate the pulse shapes and multiple times of arrival associated with an echo generated when a known pulse encounters a target of unknown impulse response. The modeled echo was assumed to have a generalized form, i.e., it was more complex than a linear combination of delayed and scaled versions of the transmitted pulse. In the short-pulse-duration algorithm developed here, it was assumed that individual events present in the echo did not overlap. For the case of the long-pulse-duration method, this assumption was removed. The techniques were tested using experimental data simulating the targets of a rigid acoustic sphere and dielectric slab, and compared with results obtained from using other methods currently available in the literature. Experimental results demonstrated that the algorithms were successful in determining the proper time delays of the echo events for a variety of received signal-to-noise ratios (S.N.R.s), and compared favorably with other techniques.

Pattern models for analyzing, representing, and compressing experimental 2D fluid flow imagery are developed. The approach is to represent flow fields using the tools of dynamical systems theory. Complex flow fields are decomposed into simple components based on the observed critical point behavior. A critical point detector based on the vector field index is developed, and its performance is analyzed. The critical point behavior is modeled by the linear phase portrait, which is a compact representation specified by a 2 x 2 A matrix. The eigenvalues of A provide a symbolic descriptor, and this allows the qualitative behavior of the critical points to be classified into one of six canonical forms. The global flow field behavior is represented using the linear phase portrait estimates as a basis. First, a linear superposition approach is considered, where the flow field is modeled using the tools of potential theory. This technique is appropriate for the representation of incompressible flows with negligible friction effects. A second approach is considered in which complex flows are modeled by nonlinear dynamical systems. A Taylor series model is assumed for the velocity components, and the model coefficients are computed by considering both local critical point and global flow field behavior. A merge and split procedure for complex flows is presented, in which patterns of neighboring critical point regions are combined and modeled. The computed models are then employed to compress scalar flow images that exhibit little or gradual variation along the flow streamlines. The model serves as a guide for removing this redundancy, and compression ratios on the order of 100:1 are achieved. Finally, the compression of vector field data using orthogonal polynomials derived from the Taylor series model is considered. A critical point scheme and a block transform are presented. They are applied to velocity fields measured in particle image velocimetry experiments and generated

The goal of image coding is to represent images with a minimum amount of distortion at a given encoding rate. Image coding algorithms comprise methods for generating uncorrelated sequences and quantizing the uncorrelated sequences. The earliest encoding algorithms, such as Differential Pulse Code Modulation, are prediction based and must be considered primitive when compared to the more recent transform coders, such as Discrete Cosine Transform or Discrete Wavelet Transform. Judged only by SNR performance, the contemporary transform coders are far superior to the predictive coders. However, the computational complexity of the transform coders is much greater than predictive coders. In general, the improvement of hardware has diminished the importance of computational complexity. Thus, little research has been devoted to improving the performance of predictive coders. Furthermore, in a few applications such as remote decoding or real-time video decoding, the complexity of the decoder is still a constraint. In this dissertation, I have developed a predictive image coder having minimal decoder complexity and providing SNR's in the range of the most advanced transform coders. The image coder utilizes the Recursive Interpolative DPCM algorithm as a kernel in conjunction with an adaptive rate allocation scheme and entropy-constrained trellis coded quantization. The Adaptive RIDPCM-ECTCQ image coder is a high performance, low decoder-complexity alternative to contemporary transform coders.

A new application of chaos to electrical engineering is developed. By creating chaotic binary sequences, and using these as pulse compression codes for radar, many advantages are realized over codes that are presently used. These chaotic codes are generated by quantizing the iterates of one-dimensional chaotic difference equations to two levels. Being chaotic, these binary sequences are unpredictable in the long term, and are nonperiodic or can have periods of billions of bits. The autocorrelations of the sequences are derived, then the sequences are applied to radar, where the unpredictable and nonperiodic nature of these sequences is exploited. It is shown that chaotic codes offer advantages in maximum range performance, range resolution, low probability of intercept, and probability of false alarm compared to codes presently used.