Optimal quantization of random measurements in compressed sensing
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
A comparative study of quantized compressive sensing schemes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
A single-letter characterization of optimal noisy compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
On the empirical rate-distortion performance of compressive sensing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
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We address the problem of encoding signals which are sparse, i.e. signals that are concentrated on a set of small support. Mathematically, such signals are modeled as elements in the \ell_pball for some p1. We describe a strategy for encoding elements of the \ell_p ball which is universal in that 1) the encoding procedure is completely generic, and does not depend on p (the sparsity of the signal), and 2) it achieves near-optimal minimax performance simultaneously for all p \le 1. What makes our coding procedure unique is that it requires only a limited number of nonadaptive measurements of the underlying sparse signal; we show that near-optimal performance can be obtained with a number of measurements that is roughly proportional to the number of bits used by the encoder. We end by briefly discussing these results in the context of image compression.