Rate-Distortion Performance of Lossy Compressed Sensing of Sparse Sources

• Published in: IEEE transactions on communications Vol. 66; no. 10; pp. 4498 - 4512
• Main Authors: Leinonen, Markus, Codreanu, Marian, Juntti, Markku, Kramer, Gerhard
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Blahut-Arimoto algorithm; conditional rate-distortion theory; Decoding; Distortion; Encoding; Error analysis; Loss measurement; Lower bounds; Noise measurement; Remote sensing; Remote sensors; Remote source coding; Resource description framework; side information; Signal reconstruction; Silicon; wireless sensor networks
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2018.2834349

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.