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The article discusses the development of a distributed Kalman filter, which is used to estimate the state of a sparsely connected, large-scale, dynamical system monitored by a network of N sensors. The discussed filter is shown to be optimal under an Lth order Gauss-Markov approximation to the centralized filter.

The algebraic signal processing theory is described, which is an axiomatic and general framework for linear signal processing. The studies have provided missing signal processing concepts associated with the discrete cosine and sine transforms and have established them as precise analogs to the discrete Fourier transforms.

A general and axiomatic approach is described for linear signal processing (SP), which is referred as to as the algebraic signal processing theory (ASP). The ASP has provided a systematic methodology for deriving fast algorithms for linear transforms.

Contrast-enhanced magnetic resonance imaging (MRI) is useful to study the infiltration of cells in vivo. This research adopts ultrasmall superparamagnetic iron oxide (USPIO) particles as contrast agents. USPIO particles administered intravenously can be endocytosed by circulating immune cells, in particular, macrophages. Hence, macrophages are labeled with USPIO particles. When a transplanted heart undergoes rejection, immune cells will infiltrate the allograft. Imaged by [T*.sub.2]-weighted MRI, USPIO-labeled macrophages display dark pixel intensities. Detecting these labeled cells in the image facilitates the identification of acute heart rejection. This paper develops a classifier to detect the presence of USPIO-labeled macrophages in the myocardium in the framework of spectral graph theory. First, we describe a USPIO-enhanced heart image with a graph. Classification becomes equivalent to partitioning the graph into two disjoint subgraphs. We use the Cheeger constant of the graph as an objective functional to derive the classifier. We represent the classifier as a linear combination of basis functions given from the spectral analysis of the graph Laplacian. Minimization of the Cheeger constant based functional leads to the optimal classifier. Experimental results and comparisons with other methods suggest the feasibility of our approach to study the rejection of hearts imaged by USPIO-enhanced MRI. Index Terms--Acute heart rejection, cardiac magnetic resonance imaging (MRI), Cheeger constant, classification, classifier, contrast agents, graph cut, graph Laplacian, spectral graph theory, ultrasmall superparamagnetic iron oxide (USPIO)-enhanced MRI.

The design of the topology of a random sensor network is presented for maximizing the convergence rate of the consensus algorithm. Results suggest the importance of the optimal design in significantly improving the convergence speed of the consensus algorithm and in achieving the performance of a non-random network at a fraction of the communication cost.

The optimization of the convergence rate of distributed algorithm by the topology given by the nonbipartite Ramanujan graphs is discussed. Results concluded that Ramanujan graphs could be prepared only for a limited number.

A systematic methodology is described for deriving and classifying fast algorithms for linear transforms. The decomposition is based on two generic methods that generalize the well-known Cooley-Tukey fast Fourier transform (FFT) and has made the algorithms' derivations concise and transparent.

We consider turbo-structured low-density parity-check (TS-LDPC) codes--structured regular codes whose Tanner graph is composed of two trees connected by an interleaver. TS-LDPC codes with good girth properties are easy to construct: careful design of the interleaver component prevents short cycles of any desired length in its Tanner graph. We present algorithms to construct TS-LDPC codes with arbitrary column weight j [greater than or equal to] 2 and row weight k and arbitrary girth g. We develop a linear complexity encoding algorithm for a type of TS-LDPC codes--encoding friendly TS-LDPC (EFTS-LDPC) codes. Simulation results demonstrate that the bit-error rate (BER) performance at low signal-to-noise ratio (SNR) is competitive with the error performance of random LDPC codes of the same size, with better error floor properties at high SNR. Index Terms--Error floor, girth, interleaver, low-density parity-check (LDPC) codes, turbo-structured.

A computationally simple and accurate method is presented for computing the error probabilities in decentralized detection in sensor networks. The application of the saddlepoint approximation is demonstrated in practical situations when the observations and local detectors are different from sensor to sensor and when the communication among sensors and the fusion center is through imperfect, noisy communication links.

The binary hypothesis test of detecting the presence or absence of a target in a highly cluttered environment is analyzed by using time reversal. The time reversal detection has provided significant gains over conventional detection, which is explained by the empirical distribution or type of the target channel frequency response.

The notion of intrinsic shape is introduced as the unique representation of the orbit containing all affine-permutation distorted shapes of the object. The blind algorithm for intrinsic shape recovery (BLAISER) is presented for recovering the intrinsic shape of the unknown object in a blind manner.

A computationally simple algorithm that segments moving objects, even in low-texture and low-contrast scenes is presented. Experiments show that the proposed algorithm could cover complex templates in low-contrast scenes.

The paper presents a novel stochastic active contour scheme (STACS) for automatic image segmentation designed to overcome some of the unique challenges in cardiac MR images such as problems with low contrast, papillary muscles, and turbulent blood flow. STACS minimizes an energy functional that combines stochastic region-based and edge-based information with shape priors of the heart and local properties of the contour. The minimization algorithm solves, by the level set method, the Euler-Lagrange equation that describes the contour evolution. STACS includes an annealing schedule that balances dynamically the weight of the different terms in the energy functional. Three particularly attractive features of STACS are: 1) ability to segment images with low texture contrast by modeling stochastically the image textures; 2) robustness to initial contour and noise because of the utilization of both edge and region-based information; 3) ability to segment the heart from the chest wall and the undesired papillary muscles due to inclusion of heart shape priors. Application of STACS to a set of 48 real cardiac MR images shows that it can successfully segment the heart from its surroundings such as the chest wall and the heart structures (the left and right ventricles and the epicardium.) We compare STACS' automatically generated contours with manually-traced contours, or the 'gold standard,' using both area and edge similarity measures. This assessment demonstrates very good and consistent segmentation performance of STACS. Index Terms--Active contour, cardiac magnetic resonance imaging (cardiac MRI), chamfer method, energy minimization, image segmentation, level set, shape and area similarities, stochastic model, stochastic relaxation.

The properties of positive definite full matrices probability whose inverses A are L-block-banded are studied. It is shown that for such matrices, the blocks in the lock-block band of probability completely determine probability, namely, all blocks of probability outside its L-block band are computed from the blocks in the L-block band of probability.

The paper describes the rank 1 weighted factorization solution to the structure from motion problem. This method recovers the 3D structure from the factorization of a data matrix that is rank 1 rather than rank 3. This matrix collects the estimates of the 2D motions of a set of feature points of the rigid object. These estimates are weighted by the inverse of the estimates error standard deviation so that the 2D motion estimates for "sharper" features, which are usually well-estimated, are given more weight, while the noisier motion estimates for "smoothed" features are weighted less. We analyze the performance of the rank I weighted factorization algorithm to determine what are the most suitable 3D shapes or the best 3D motions to recover the 3D structure of a rigid object from the 2D motions of the features. Our approach is developed for the orthographic camera model. It avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences. Experimental studies with synthetic and real data illustrate the good performance of our approach. Index Terms--Factorization methods, structure from motion, image sequence analysis, rigid body motion, uncertainty in motion analysis, power method, weighted factorization.

A new procedure for estimating of 3-D rigid shape and 3-D motion from a 2-D video sequence is proposed. A computationally simple algorithm performs well, which is illustrated by two experiments with real-life video.

This work designs sequence detectors for channels with intersymbol interference (ISI) and correlated (and/or signal-dependent) noise. We describe three major contributions, i) First, by modeling the noise as a finite-order Markov process, we derive the optimal maximum-likelihood sequence detector (MLSD) and the optimal maximum a posteriori (MAP) sequence detector, extending to the correlated noise case the Viterbi algorithm. We show that, when the signal-dependent noise is conditionally Gauss-Markov, the branch metrics in the MLSD are computed from the conditional second-order noise statistics. We evaluate the branch metrics using a bank of finite impulse response (FIR) filters, ii) Second, we characterize the error performance of the MLSD and MAP sequence detector. The error analysis of these detectors is complicated by the correlation asymmetry of the channel noise. We derive upper and lower bounds and computationally efficient approximations to these bounds based on the banded structure of the inverses of Gauss-Markov covariance matrices. An experimental study shows the tightness of these bounds, iii) Finally, we derive several classes of suboptimal sequence detectors, and demonstrate how these and others available in the literature relate to the MLSD. We compare their error rate performance and their relative computational complexity, and show how the structure of the MLSD and the performance evaluation guide us in choosing a best compromise between several types of suboptimal sequence detectors. Index Terms: Correlated noise, Gauss-Markov processes, intersymbol interference, Markov channel noise, Markov memory, maximum-likelihood sequence detection, Viterbi algorithm.

A method is presented for combining underlying model dynamics with measurements in physical sciences such as oceanography and meteorology. The process is based on using the sparseness of the measurements and the block structure of the underlying model dynamics to develop new implementations of the Kalman-Bucy filter.

A study was conducted to identify which random models commensurate to the discrete cosine transform (DCT) and the discrete sine transform (DST). Results showed that the DST and DCT transforms are asymptotically equivalent to homeogenous one-dimensional and two-dimensional Gauss noncausal Markov random fields, which are characterized on finite lattices with appropriate boundary conditions.

In high density magnetic recording, noise samples corresponding to adjacent signal samples are heavily correlated as a result of front-end equalizers, media noise, and signal nonlinearities combined with nonlinear filters to cancel them. This correlation significantly deteriorates the performance of detectors at high densities. In this paper, we propose a novel sequence detector that is correlation sensitive and adaptive to the nonstationary signal sample statistics. We derive the correlation-sensitive maximum likelihood detector. It can be used with any Viterbi-like receiver (e.g., partial response maximum likelihood, fixed delay tree search, multilevel decision feedback equalization) that relies on a tree/trellis structure. Our detector adjusts the metric computation to the noise correlation statistics. Because these statistics are nonstationary, we develop an adaptive algorithm that tracks the data correlation matrices. Simulation results are presented that show the applicability of the new correlation-sensitive adaptive sequence detector. Index Terms - Adaptive, correlation sensitive, maximum likelihood sequence detection, signal dependent.

A geometric framework which utilizes wavelet-resolution-based techniques may be utilized in designing a receiver that can handle signal models discrepancies. The receiver may function as a focused detector which may function effectively in a multipath environments which degrades the detection performance of conventional receiver. The innovative detector utilizes as test statistic the energy of the projection a received signal on the multipath signal.

A new blind algorithm for advanced space division multiple access (SDMA) in mobile communication systems is presented. Array channel division multiple access (AChDMA) improves system capacity by increasing its time and frequency reuse. AChDMA distinguishes the moving sources by tracking their multipath configuration and resolving their distinct generalized steering vectors. It optimizes a finite mixture log-likelihood function, combining an efficient initialization process with an EM-based algorithm that offers fast convergence to the global maximum.

A study was conducted to introduce a new definition of ambiguity function based on a geometric interpretation of maximum likelihood parameter estimation with exponential families and on concepts of information theory. The new definition is equivalent to Woodward's radar narrow-band ambiguity function for the active single target problem. However, the new ambiguity can handle radar/sonar problems when there are unknown parameters and when the signals are random or wideband.

In this paper, we study the statistics of zig-zag transition walls in digital magnetic recording and their relationship to transition noise defining quantities. We provide analytic results that link the statistics of zig-zag transitions to media/recording parameters. The basis of our study is the triangle zig-zag transition (TZ-ZT) model due to its well-defined triangle zig-zag shape and its cross-track stability. The results we derive here, however, are of a general nature, and given the right interpretation, apply to other zig-zag models as well, as we show in the paper. We also provide an interpretation of the cross-track correlation width, linking this quantity to the statistics of magnetized clusters in thin-film magnetic media. The paper concludes by showing how these results can be used in media noise modeling.

A multipath signal detection algorithm which does not require maximum likelihood estimates while still providing good performance is presented. The technique is based on a geometric interpretation of the multipath detection problem. A representation subspace G, that is matched to the multipath signal subspace S in the gap sense, is developed. Only the case where the transmitted signal is completely known is investigated.

A noncausal predictive image codec based on a noncausal prediction model alongwith vector quantization is more efficient in image compression than conventional causal predictors. An equivalent unilateral transformation of the noncausal model provides the advantages of recursive processing. This does not affect the optimality of the noncausal model. The causal predictor produces reconstructed images with high amount of streaking, while those produced by the noncausal predictor does not contain streaking. The codec gives high-quality compressed images at low bit rates.

We describe a technique for still image compression that combines i) noncausal optimal recursive prediction, ii) residual quadtree mean removal, and iii) a modification of cascaded vector quantization. We refer to this image codec as noncausal prediction with residual mean removal, and cascaded vector quantization (NRQ/CVQ). We provide examples that illustrate the performance of NRQ/CVQ up to compression ratios of 42.5:1. We show that NRQ/CVQ outperforms alternative algorithms that we tested including the conventional causal prediction differential pulse code modulation (DPCM) with quadtree mean removal cascaded vector quantization and the Joint Photographic Experts Group (JPEG) baseline standard algorithm.

An inverse problem method, used in the design of beam forming structures, enables the determination of a waveform estimate through a space/time processor. The determination requires a group of noisy temporal and spatial measurements which are subjected to certain optimization conditions. The l1 and l2 norms form the basis for the inversion strategies used in the inverse problem method.

The parameter structure of noncausal homogeneous Gauss Markov random fields (GMRF) defined on finite lattices is studied. For first-order (nearest neighbor) and a special class of second-order fields, we provide a complete characterization of the parameter space and a fast implementation of the maximum likelihood (ML) estimator of the field parameters. For general higher order fields, tight bounds for the parameter space are presented and an efficient procedure for ML estimation is described. Experimental results illustrate the application of the approach presented and the viability of the present method in fitting noncausal models to 2-D data.

This paper describes a new type of regular structured low-density parity-cheek (LDPC) code: the partition-and-shift LDPC (PS-LDPC) code. PS-LDPC codes can be easily designed to have large girth. The code construction is simple to explain: we divide the bit and check nodes in the Tanner graph into subsets and connect nodes in these subsets according to a set of parameters called shifts. We derive a general theorem on the shifts to prevent cycles that are harmful to LDPC decoding. This theorem provides a methodology to design PS-LDPC codes with arbitrary column weight j and large girth g. Simulation results over EPR4 channels demonstrate the good bit-error rate performance of PS-LDPC codes. Index Terms--Error floor, girth, low-density parity-check (LDPC).

The triangle zig-zag transition (TZ-ZT) model is a stochastic zig-zag transition model. It is a fast alternative to micromagnetic modeling. Thus far, the TZ-ZT model has been compared only to the micromagnetic model. Here we compare the model to real data and validate its signal and noise modeling capability.

We propose the triangle zig-zag transition (TZ-ZT) model as a faster alternative to micro-magnetic media modeling. We present equations that relate the statistics of the TZ-ZT model to recording process parameters. Both isolated and interacting transitions are modeled. Simulation results show the performance of the model.

Research is presented concerning the use of second-order statistics for the development of a blind closed-form consistent channel estimator for systems consisting of multiple-input multiple-out channels.

A new study seeks to design an adaptive anomaly detection algorithm for use in hyperspectral imagery.

The problem of approximating arbitrary, discrete-time, Gaussian random processes by a representative wavelet-based Gaussian method is considered. For this purpose, the similarity between the original processes and the proposed algorithm is measured with the Bhattacharyya coefficient. The Bhattacharyya coefficient is used to reduce the task of defining the representative process to determining an optimal unitary matrix of wavelet-based eigenvectors, a mean vector and an associated diagonal matrix of eigenvalues. The resulting matching algorithm maximizes the nonadditive Bhattacharyya coefficient.

A study was conducted to analyze subspace representations robust to translations of the input signal. Robustness was determined based on the mean square error, signal representations and arbitrary delays. Robust scaling functions were represented as the minimizers to accommodate errors based on the coefficients of the two-scale equation. Results indicated algorithms that can be utilized to obtain robust scaling functions.

Discusses the development of the optimal Bayesian detector/tracker for rigid extended targets that move randomly in clutter. Models for sensor, target, motion and clutter used in the study; Derivation of the optimal Bayesian detector/tracker; Quantification of the detection and tracking performances of the algorithm through comprehensive Monte Carlo simulations assuming a single target scenario.

Presents a study which examined the inversion of full matrices whose inverse are L-banded. Discussion on the banded matrix algebra; Representations of Gauss-Markov random processes; Summary.

Studies the statistics of zig-zag transition walls in digital magnetic recording and their relationship to transition noise defining quantities. Brief review of triangle zig-zag transition (TZ-ZT) model and other proposed stochastic zig-zag transition models; Statistical relationship of zig-zag patterns to measurable media or recording quantities.