Ten lectures on wavelets
Source Coding with Quantized Redundant Expansions: Accuracy and Reconstruction
DCC '99 Proceedings of the Conference on Data Compression
Optimal Multiple Description Transform Coding of Gaussian Vectors
DCC '98 Proceedings of the Conference on Data Compression
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms
IEEE Transactions on Information Theory
Efficient quantization for overcomplete expansions in RN
IEEE Transactions on Information Theory
Resilience properties of redundant expansions under additive noise and quantization
IEEE Transactions on Information Theory
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Abstract: In this paper, we study the construction of structured regular quantizers for overcomplete expansions in RN. Our goal is to design structured quantizers allowing simple reconstruction algorithms with low (memory and computational) complexity and having good performance in terms of accuracy. Most related work to date in quantized redundant expansions has assumed that uniform scalar quantization with the same stepsize was used on the redundant expansion and then has dealt with more complex methods to improve the reconstruction. Instead, we consider the design of scalar quantizers with different stepsizes for each coefficient of an overcomplete expansion in such a way as to produce an equivalent vector quantizer with periodic structure. The periodicity makes it possible to achieve good accuracy using simple reconstruction algorithms from the quantized coefficients of the overcomplete expansion.