Rate-distortion performance of lossy compressed sensing of sparse sources

We investigate lossy compressed sensing (CS) of a hidden, or remote, source, where a sensor observes a sparse information source indirectly. The compressed noisy measurements are communicated to the decoder for signal reconstruction with the aim to minimize the mean square error distortion. An analytically tractable lower bound to the remote rate-distortion function (RDF), i.e., the conditional remote RDF, is derived by providing support side information to the encoder and decoder. For this setup, the best encoder separates into an estimation step and a transmission step. A variant of the Blahut-Arimoto algorithm is developed to numerically approximate the remote RDF. Furthermore, a novel entropy coding based quantized CS method is proposed. Numerical results illustrate the main rate-distortion characteristics of the lossy CS, and compare the performance of practical quantized CS methods against the proposed limits.

Authors:
Leinonen Markus, Codreanu Marian, Juntti Markku, Kramer Gerhard

Publication type:
A1 Journal article – refereed

Place of publication:

Keywords:
Blahut-Arimoto algorithm, conditional rate-distortion theory, Remote source coding, side information, Wireless sensor networks

Published:

Full citation:
M. Leinonen, M. Codreanu, M. Juntti and G. Kramer, “Rate-Distortion Performance of Lossy Compressed Sensing of Sparse Sources,” in IEEE Transactions on Communications, vol. 66, no. 10, pp. 4498-4512, Oct. 2018. doi: 10.1109/TCOMM.2018.2834349

DOI:
https://doi.org/10.1109/TCOMM.2018.2834349

Read the publication here:
http://urn.fi/urn:nbn:fi-fe2018112348888