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Parallel implementations of Jacobi algorithm for eigenanalysis of a matrix on most commonly used high performance computing (HPC) devices such as central processing unit (CPU), graphics processing unit (GPU), and field-programmable gate array (FPGA) are discussed in this paper. Their performances are investigated and compared. It is shown that CPU, even with multi-threaded implementation, is not a feasible option for large dense matrices. For the GPU implementation, performance impact of the global memory access patterns on the GPU board and the memory coalescing are emphasized. Three memory access methods are proposed. It is shown that one of them achieves 81.6% computational performance improvement over the traditional GPU methods, and it runs 68.5 times faster than a single-threaded CPU for a dense symmetric square matrix of size 1,024. Furthermore, FPGA implementation is presented and its performance running on chips from two major manufacturers are reported. A comparison of GPU and FPGA implementations is quantified and ranked. It is reported that FPGA design delivers the best performance for such a task while GPU is a strong competitor requiring less development effort with superior scalability. We predict that emerging big data applications will benefit from real-time and high performance computing implementations of eigenanalysis for information inference and signal analytics in the future.

The high peak-to-average power ratio (PAPR) of the transmitted signal is a major drawback of multicarrier transmission such as orthogonal frequency-division multiplexing OFDM. A plethora of PAPR reduction techniques has been reported in the literature. Some of the techniques modify the phase and/or amplitude of symbols in the original symbol alphabet (SA) such as selected mapping and partial transmit sequences techniques. However, such methods have shortcomings of a heavy computational burden caused by required multiple inverse fast-Fourier transform (IFFT) operations and bit error rate performance degradation due to side information (SI). In this study, a low-complexity PAPR reduction framework is proposed to jointly modify phase and amplitude values of the original symbols in the alphabet. This framework utilises only one IFFT/FFT operator pair for transmultiplexing of symbols without any SI. The merit of the proposed method to design a SA modifier matrix (SAM) for PAPR reduction is shown through performance comparisons for the application scenarios presented in this study.

We propose sparse Karhunen–Loeve Transform (SKLT) method to sparse eigen subspaces. The sparsity (cardinality reduction) is achieved through the pdf-optimized quantization of basis function (vector) set. It may be considered an extension of the simple and soft thresholding (ST) methods. The merit of the proposed framework for sparse representation is presented for auto-regressive order one, AR(1), discrete process and empirical correlation matrix of stock returns for NASDAQ-100 index. It is shown that SKLT is efficient to implement and outperforms several sparsity algorithms reported in the literature.

Signal dependent Karhunen-Loeve transform (KLT), also called factor analysis or principal component analysis (PCA), has been of great interest in applied mathematics and various engineering disciplines due to optimal performance. However, implementation of KLT has always been the main concern. Therefore, fixed transforms like discrete Fourier (DFT) and discrete cosine (DCT) with efficient algorithms have been successfully used as good approximations to KLT for popular applications spanning from source coding to digital communications. In this paper, we propose a simple method to derive explicit KLT kernel, or to perform PCA, in closed-form for first-order autoregressive, AR (1), discrete process. It is a widely used approximation to many real world signals. The merit of the proposed technique is shown. The novel method introduced in this paper is expected to make real-time and data-intensive applications of KLT, and PCA, more feasible.

A regional hidden Markov model (RHMM) for automatic facial expression recognition in video sequences is proposed. Facial action units are described by RHMMs for the states of facial regions: eyebrows, eyes and mouth registered in a video. The tracked facial feature points in the spatial domain form observation sequences that drive the classification process. It is shown that the proposed technique outperforms other methods reported in the literature for the person-independent case tested with the extended Cohn-Kanade database.

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in several engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. In this paper, we present a generalized framework for DFT called Generalized DFT (GDFT) with nonlinear phase by exploiting the phase space. We show that GDFT offers sizable correlation improvements over DFT, Walsh, Oppermann and Gold codes, leading to better performance in all multi-carrier communications scenarios investigated. We also highlight how known constant modulus orthogonal transforms are special solutions of the proposed GDFT framework. Moreover, we introduce practical design methods offering computationally efficient implementations of GDFT as enhancements to DFT. We conclude the paper with examples of communications applications where GDFT is shown to outperform DFT and other known constant modulus bases.

Walsh codes are perfectly orthogonal binary (antipodal) block codes that found their use in many popular applications over several decades including synchronous multiuser communications. It is well known in the literature that they perform poorly for the case of asynchronous multiuser communications. Therefore, the near-orthogonal and nonlinear phase gold codes with better performance are the preferred user codes in asynchronous direct sequence code division multiple access (DS-CDMA) communications standards. In this paper, we relaxed linear phase requirements and new sets of Walsh-like nonlinear phase binary orthogonal user codes (transforms) are obtained for asynchronous and synchronous spread spectrum multiuser communications. It is shown that the proposed binary user code family outperforms the Walsh codes significantly and they match in performance with the popular, nearly orthogonal gold codes closely for asynchronous multiuser communications in additive white Gaussian noise (AWGN) channels. It is also shown that all of the binary code families considered in this paper performed comparable for Rayleigh flat-fading channels. We present in this paper that there are a good number of such desirable code sets available in the binary sample space with different transform sizes. These new binary sets with good performance and flexible code lengths might help us to improve the spread spectrum multiplexing capabilities of future wireline and wireless CDMA communications systems.

Speckle decorrelation analysis of optical coherence tomography (OCT) signal has been used in motion tracking. In our previous study, we demonstrated that cross-correlation coefficient (XCC) between Ascans had an explicit functional dependency on the magnitude of lateral displacement (δx). In this study, we evaluated the sensitivity of speckle motion tracking using the derivative of function XCC(δx) on variable δx. We demonstrated the magnitude of the derivative can be maximized. In other words, the sensitivity of OCT speckle tracking can be optimized by using signals with appropriate amount of decorrelation for XCC calculation. Based on this finding, we developed an adaptive speckle decorrelation analysis strategy to achieve motion tracking with optimized sensitivity. Briefly, we used subsequently acquired Ascans and Ascans obtained with larger time intervals to obtain multiple values of XCC and chose the XCC value that maximized motion tracking sensitivity for displacement calculation. Instantaneous motion speed can be calculated by dividing the obtained displacement with time interval between Ascans involved in XCC calculation. We implemented the above-described algorithm in real-time using graphic processing unit (GPU) and demonstrated its effectiveness in reconstructing distortion-free OCT images using data obtained from a manually scanned OCT probe. The adaptive speckle tracking method was validated in manually scanned OCT imaging, on phantom as well as in vivo skin tissue.

In this paper, we investigate the general problem of data hiding and propose an approach for effective cover noise interference rejection in oblivious applications. We first evaluate the performance in the commonly used direct sequence modulation approach where a low-power signal is embedded into the original cover signal. The optimal detection is derived and its performance is analyzed. Second, we study a novel approach in oblivious data hiding and evaluate its performance and compare it with existing algorithms. Both simulation studies and empirical data hiding results validate its efficiency in the multimedia oblivious applications.

This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics.

It is well known that a proper interference exciser enhances the performance of a spread spectrum communications system. There have been several competing excision techniques reported in the literature. This article presents a performance evaluation of those excision techniques via the analytical and computer simulation tools. It is found that the analytical performance tools presented match up with the computer simulation results. It is also shown that a previously proposed adaptive time-frequency exciser consistently outperforms the existing interference excision techniques in the literature.

Subband and wavelet transforms have been a subject of great interest, especially in the fields of signal processing and applied mathematics. This article presents a tutorial on this subject, emphasizing the fundamentals and the reason for its success, importance, and potential. Subband and wavelet transform applications in communications are also reviewed. These application areas include interference excision, spread spectrum codes based on subband transform bases, CDMA, and discrete multitone transceivers.

Orthogonal transmultiplexers have been successfully utilized for multiuser communications. They are of the FDMA type in their most common version. The transmultiplexers using frequency selective PR-QMFs as their user codes were reported in the literature. This approach conflicts with the requirements of a CDMA communications system. We introduce novel spread spectrum PR-QMF codes, wherein the orthogonality is distributed over both time and frequency domains. It is shown that the proposed multivalued spread spectrum PR-QMF codes with minimized auto and cross-correlation properties outperform the conventional binary Gold codes in CDMA communication scenarios considered in the article.

This correspondence deals with suboptimal multiplierless perfect reconstruction quadrature mirror filter (PR-QMF) solutions. It is shown that multiplierless PR-QMFs perform comparable to or better than the known filter banks and discrete-cosine-transform-based (DCT-based) image coding techniques objectively and subjectively. They are very efficient to implement on very large scale integrated (VLSI) systems. These PR-QMFs might find uses in real-time image and video coding and other applications.

A smart time-frequency exciser for DS-SS communications is proposed in this correspondence. This technique utilizes the concept of uncertainty in time-frequency analysis of signals. It brings the novel concept of domain switchable signal processing. Hence, the adaptive time-frequency (ATF) exciser has the capability of deciding the domain of the interference cancellation. Additionally, adaptive subband transforms are utilized for frequency domain excision. For time-domain excision, the ATF excision algorithm utilizes a sliding time window to reject the nonstationary, pulsed (time-localized) interference. It is shown that the proposed adaptive time-frequency exciser-based DS-SS communications receiver drastically outperforms the existing systems. Its performance is nearly optimal and very robust to the inter and intradomain variations of the undesired signal.

The article deals with spectral modeling in filter banks. It is shown, both theoretically and experimentally, that subspectral modeling is superior to full spectrum modeling if performed before the rate change. The price paid for this performance improvement is an increase of computations. A few different signal sources were considered in this study. It is shown that the performance of AR and ARMA techniques are comparable in subspectral modeling. The first is desired because of its simplicity. As an application of this study, we implemented a CELP based speech codec embedded in a filter bank structure. We found that there were no performance improvements of subband CELP technique over the fullband case. The theoretical reasonings of the experimental results are also given.

Portfolio risk, introduced by Markowitz in 1952 and defined as the standard deviation of the portfolio return, is an important metric in the modern portfolio theory (MPT). A popular method for portfolio selection is to manage the risk and return of a portfolio according to the cross-correlations of returns for various financial assets. In a real-world scenario, estimated empirical financial correlation matrix contains significant level of intrinsic noise that needs to be filtered prior to risk calculations. © 2011 IEEE.

A generalized, parametric, perfect-reconstruction quadrature-mirror-filter (PR-QMF) design technique based on Bernstein polynomial approximation in the magnitude-square domain is presented. The parametric nature of this solution provides useful insights to the PR-QMF problem. Several well-known orthonormal wavelet filters, PR-QMFs, are shown to be the special cases of the proposed technique. Energy compaction performances of a few popular signal decomposition techniques are presented for AR(1) signal sources. It is observed that the hierarchical QMF filter banks considered outperform the block transforms as expected. >

The energy compaction performance of several lapped orthogonal transforms (LOTs) are presented. It is shown that the LOT outperforms the conventional block transforms for all the cases considered. The performance of the poorly performing block transforms for high correlation sources increased dramatically in their LOT versions. It is found that the energy compaction performance of the LOT versions of the different block transforms considered is about the same. Therefore, the choice of LOT is based on the efficiency of the transform algorithm. The LOT is an alternative to the block transforms for signal coding applications. Also, the blocking effect is reduced with the increase in the computational complexity of the transform algorithm. >

The authors derive a matrix factorization of the coefficient variances for any fixed transformation. This factorization formulation provides a better framework for understanding the role of transform on the one hand, and the signal source model on the other. It also greatly simplifies the number of computational operations required for each variance calculation. A transform-specific matrix which links the transform to the signal correlation model is derived. This factorization provides a conceptual framework for understanding the behaviour of the transform for different source models. It also significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices. This simplification can be used in adaptive transform coding which requires an estimate of the variances. Test results demonstrate that this mode-based variance calculation provides an accurate basis for adaptive transform coding, particularly at low bit rates. >

In this paper, we present an information-theoretic approach to obtain an estimate of the number of bits that can be hidden in still images, or, the capacity of the data-hiding channel.We show how the addition of the message signal or signature in a suitable transform domain rather than the spatial domain can significantly increase the channel capacity. Most of the state-of-the-art schemes developed thus far for data-hiding have embedded bits in some transform domain, as it has always been implicitly understood that a decomposition would help. Though most methods reported in the literature use DCT or wavelet decomposition for data embedding, the choice of the transform is not obvious.We compare the achievable data-hiding capacities for different decompositions like DCT, DFT, Hadamard, and subband transforms and show that the magnitude DFT decomposition performs best among the ones compared.

The authors propose a simple fast-search VQ of the LSFs to be used on top of the split VQ, that is, in each of the sub-vector domains. The main trait of the proposed method is that no suboptimal codebooks are used and there is no further reduction in performance. In each sub-vector domain, a full-size optimally trained codebook typically of size 1024, is searched using a fast-search algorithm. The result of this search is identical to that of a full-search, yet, only about 25% of a full-search complexity is needed.

A class of audio-visual content is segmented into dialogue scenes using the state transitions of a novel hidden Markov model (HMM). Each shot is classified using both the audio track and the visual content to determine the state/scene transitions of the model. After simulations with circular and left-to-right HMM topologies, it is observed that both performing very well with multi-modal inputs. Moreover, for the circular topology, the comparisons between different training and observation sets show that audio and face information together gives the most consistent results among different observation sets.

In this paper, we present a novel switch design of a large scale multicast packet switch which is featured by a modular switch architecture and a distributed resource allocation algorithm. Switch inputs and outputs are grouped into small modules called Input Shared Blocks (ISBs) and Output Shared blocks (OSBs). Input link sharing and output link sharing are cooperated intelligently so that no speedup is necessary in central switch fabric (ATMCSF). Cell delivery is based on link reservation in every ISB. Dual round robin rings connect ISBs to provide a fast and fair link resource allocation among ISBs according to a Queue Occupancy Based Dynamic Link Reservation (QOBDLR) algorithm. QOBDLR is a distributed algorithm in which an ISB can dynamically increase/decrease its link reservation for a specific OSB according to its local available information. Arbitration complexity is O(1). Switch performance is evaluated through simulations for an 256×256 switch. It is demonstrated that the proposed switch can achieve a comparable performance as the output queued switch under any traffic pattern.

A density evolution procedure for low-density parity-check (LDPC) codes under Max-Log-MAP decoding is presented. Using this technique, the precise convergence threshold for LDPC code could be easily derived.

Perfect reconstruction quadrature mirror filters (PR QMF’s) have been proposed as structures suitable for hierarchical subband coding [ ll-[4], and also for multiresolution signal decomposition as might be used in image pyramid coding [5]. More recently, multiresolution signal decomposition methods are being examined from the standpoint of the discrete wavelet transform for continuous-time signals [6]-[8]. In this paper, we describe a class of orthogonal binomial filters that provide basis functions for a perfect reconstruction bank of finite impulse response QMF’s. The orthonormal wavelet filters derived by Daubechies 171 from a discrete wavelet transform approach are shown to be the same as the solutions inherent in the binomial-based filters. The energy compaction performance of the binomial QMF decomposition is computed and shown to be better than the DCT for the Markov source models, as well as real-world images considered. The proposed binomial structure is efficient, simple to implement on VLSI, and suitable for multiresolution signal decomposition and coding applications.

The majority of the existing data hiding schemes are based on the direct-sequence (DS) modulation where a low-power random sequence is embedded into the original cover signal to represent hidden information. In this paper, we investigate linear and nonlinear modulation approaches in digital data hiding. One typical DS modulation algorithm is explored and its optimal oblivious detector is derived. The results expose its poor cover noise suppression as the hiding signature signal always has much lower energy than the cover signal. A simple nonlinear algorithm, called set partitioning, is proposed and its performance is analyzed. Analysis and simulation studies further demonstrate improvements over the existing schemes.