AG Kommunikationstheorie


Almost Lossless Compression of Analog Sources


Compressive sensing provides guarantees for complete recovery of sparse vectors from measurements of smaller dimension. In this talk, compressive sensing problem is seen in a new light, interpreted as lossless compression of analog sources. An information theoretic setup for lossless compression of analog sources is introduced, and the problem of lossless compression is understood as densest fine covering of a region of space with most of the probability concentrated on it. The dimension compression, or in compressive sensing term, how small the number of measurements can be, turns out to be related to Renyi information dimension of the source. For stochastic sparse sources, the information dimension coincides with the sparsity degree of the source, verifying compressive sensing results.

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