Distributed Distortion-Rate Optimized Compressed Sensing in Wireless Sensor Networks

Abstract

This paper addresses lossy distributed source coding for acquiring correlated sparse sources via compressed sensing (CS) in wireless sensor networks. Noisy CS measurements are separately encoded at a finite rate by each sensor, followed by the joint reconstruction of the sources at the decoder. We develop a novel complexity-constrained distributed variable-rate quantized CS method, which minimizes a weighted sum between the mean square error signal reconstruction distortion and the average encoding rate. The encoding complexity of each sensor is restrained by pre-quantizing the encoder input, i.e., the CS measurements, via vector quantization. Following the entropy-constrained design, each encoder is modeled as a quantizer followed by a lossless entropy encoder, and variable-rate coding is incorporated via rate measures of an entropy bound. For a two-sensor system, necessary optimality conditions are derived, practical training algorithms are proposed, and complexity analysis is provided. Numerical results show that the proposed method achieves superior compression performance as compared with baseline methods, and lends itself to versatile setups with different performance requirements.