Rate-distortion function upper bounds for Gaussian vectors and their applications in coding AR sources

source coding; rate-distortion function (RDF); Gaussian vector; autoregressive (AR) source; discrete Fourier transform (DFT

An Upper Bound to Zero-Delay Rate Distortion via Kalman Filtering for Vector Gaussian Sources

We deal with zero-delay source coding of a vector Gaussian autoregressive (AR) source subject to an average mean squared error (MSE) fidelity criterion. Toward this end, we consider the nonanticipative rate distortion function (NRDF) which is a lower bound to the causal and zero-delay rate distortion function (RDF). We use the realization scheme with feedback proposed in [1] to model the corresponding optimal "test-channel" of the NRDF, when considering vector Gaussian AR(1) sources subject to an average MSE distortion. We give conditions on the vector Gaussian AR(1) source to ensure asymptotic stationarity of the realization scheme (bounded performance). Then, we encode the vector innovations due to Kalman filtering via lattice quantization with subtractive dither and memoryless entropy coding. This coding scheme provides a tight upper bound to the zero-delay Gaussian RDF. We extend this result to vector Gaussian AR sources of any finite order. Further, we show that for infinite dimensional vector Gaussian AR sources of any finite order, the NRDF coincides with the zero-delay RDF. Our theoretical framework is corroborated with a simulation example.Comment: 7 pages, 6 figures, accepted for publication in IEEE Information Theory Workshop (ITW

Conjoint probabilistic subband modeling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1997.Includes bibliographical references (leaves 125-133).by Ashok Chhabedia Popat.Ph.D

Rate-distortion function upper bounds for Gaussian vectors and their applications in coding AR sources

source coding; rate-distortion function (RDF); Gaussian vector; autoregressive (AR) source; discrete Fourier transform (DFT

Improvements to sparse signal processing in compressive sensing and other methods

Compressive Sensing (CS), as a newly developed branch of sparse signal processing and representation approaches, has quickly found various applications in a large number of research topics in modern digital signal processing area. This work is devoted to investigating some effective CS and sparse signal processing schemes and approaches, and also to adapting the sparse signal processing idea and CS framework to some specific applications such as object-based surveillance video compression. In compressive sensing, the sampling strategy and reconstruction algorithms are two major components. In this thesis, we first investigate the optimization of the sampling matrix for effective CS performance. An optimizing method, by using a simple polynomial shrink function and a detector to estimate the convergence to stop the iterations early, is proposed to provide better CS performance. A number of experimental simulations are presented to demonstrate the optimized measurement matrix’s effectiveness. Then, a novel Backtracking-based Adaptive Orthogonal Matching Pursuit (BAOMP) method is proposed to effectively reconstruct or approximate the sparse solutions for CS and other sparse representation problems. Different from other Orthogonal Matching Pursuit (OMP)-type algorithms, the proposed method incorporates a backtracking step to more carefully choose the reliable support set, and at the same time, it does not require the signal’s sparsity level to be known before reconstruction. Various experiments on exact sparse signal reconstruction case, noisy signal or noisy measurement approximation case, and two-dimensional (2-D) compressible signal approximation case are illustrated to show the better performance than that of other known OMP-type methods. Furthermore, as an application of CS approach and sparse signal processing idea, an object-based surveillance video compression system based on CS is proposed, in which the sparse object error after motion compensation is coded by using CS scheme. In the proposed system, first the front-moving objects are segmented from background, then these are object-based compensated from previous reconstructed frames, and finally the object error blocks are encoded by CS approach and quantized to transmit or store. Extensive experiments show the proposed system’s efficiency. Finally, a simple iterative reconstruction method based on Projection Onto Convex Sets (POCS) is designed to effectively encode the object error. Firstly, we consider the reconstruction performance of one-dimensional (1-D) Autoregressive (AR) source signal, and then use a natural image as the input signal to do some experiments to illustrate the proposed method’s performance on image reconstruction. Finally, as an application of the iterative reconstruction method, a novel sparse signal compression scheme based on this iterative method is presented.DOCTOR OF PHILOSOPHY (EEE