A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
The SVD and reduced rank signal processing
Signal Processing - Theme issue on singular value decomposition
Abstract Optimal Linear Filtering
SIAM Journal on Control and Optimization
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
Best approximation of the identity mapping: The case of variable finite memory
Journal of Approximation Theory
Optimal multilinear estimation of a random vector under constraints of causality and limited memory
Computational Statistics & Data Analysis
Filtering and compression for infinite sets of stochastic signals
Signal Processing
Towards theory of generic Principal Component Analysis
Journal of Multivariate Analysis
Computational Methods for Modeling of Nonlinear Systems
Computational Methods for Modeling of Nonlinear Systems
Generic weighted filtering of stochastic signals
IEEE Transactions on Signal Processing
Wavelets and filter banks: theory and design
IEEE Transactions on Signal Processing
Relative Karhunen-Loeve transform
IEEE Transactions on Signal Processing
Maximum likelihood parameter and rank estimation in reduced-rankmultivariate linear regressions
IEEE Transactions on Signal Processing
Wavelet footprints: theory, algorithms, and applications
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Optimal reduced-rank estimation and filtering
IEEE Transactions on Signal Processing
The Distributed Karhunen–Loève Transform
IEEE Transactions on Information Theory
Dimensionality Reduction for Distributed Estimation in the Infinite Dimensional Regime
IEEE Transactions on Information Theory
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Data compression techniques mainly consist of two operations, data compression itself and a consequent data de-compression. In real time, the compressor and de-compressor are causal and, at a given time, may process (or 'remember') only a fragment of the input signal. In the latter case, we say that such a filter has a finite memory. We study a new technique for optimal real-time data compression. Our approach is based on a specific formulation of two related problems so that one problem is stated for data compression and another one for data de-compression. A compressor and de-compressor satisfying conditions of causality and memory are represented by matrices with special forms, A and B, respectively. A technique for the solution of the problems is developed on the basis of a reduction of minimization problems, in terms of matrices A and B, to problems in terms of specific blocks of A and B. The solutions represent data compressor and data de-compressor in terms of blocks of those matrices that minimize associated error criteria. The analysis of the associated errors is also provided.