Distributed Distortion-Rate Optimized Compressed Sensing in Wireless Sensor Networks

Abstract

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 joint reconstruction of the sources at the decoder. We develop a novel complexity-constrained distributed variablerate 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 variablerate 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 to baseline methods, and lends itself to versatile setups with different performance requirements.Index Terms-Distributed lossy source coding, joint sparsity, entropy-constrained vector quantization, variable-length coding, rate measure.

Practical Compression Methods for Quantized Compressed Sensing

“…based QCS algorithms have been devised in, e.g., [14,21,[27][28][29][30]. The related informationtheoretic studies include [14,31,32].…”

“…2) A variable-rate quantizer minimizes a cost function (6) where is given in (3), and is an RD tradeoff parameter. Following the principles of entropy-constrained scalar/vector quantization (ECSQ/ECVQ) [19][20][21], can be trained by the three-step iterative loop presented in Algorithm 3. The online phase is presented in Algorithm 4.…”

Energy‐efficient data transmission technique for wireless sensor networks based on DSC and virtual MIMO

“…The concept of the DSC is based on the SW coding theorem. Accordingly, the effective compression of, at least two sources can be accomplished by separate encoding and combined decoding [16–18].…”

Distributed Quantization for Sparse Time Sequences

“…Compressed sensing (CS) studies reconstruction of sparse signals from lower dimensional projections [17]. Distributed CS was studied in [18]- [22], sparse recovery from quantized projections was considered in [23]- [29], while [30], [31] proposed vector quantization schemes for bit-constrained distributed CS. Despite the similarity, there is a fundamental difference between distributed quantization of sparse signals and distributed CS with quantized observations: In the quantization framework, the measurements are the sparse signals, while in CS the observations are a linear projection of the signals.…”