Graded Quantization for Multiple Description Coding of Compressive Measurements

Abstract

Compressed sensing (CS) is an emerging paradigm for acquisition of compressed representations of a sparse signal. Its low complexity is appealing for resource-constrained scenarios like sensor networks. However, such scenarios are often coupled with unreliable communication channels and providing robust transmission of the acquired data to a receiver is an issue. Multiple description coding (MDC) effectively combats channel losses for systems without feedback, thus raising the interest in developing MDC methods explicitly designed for the CS framework, and exploiting its properties. We propose a method called Graded Quantization (CS-GQ) that leverages the democratic property of compressive measurements to effectively implement MDC, and we provide methods to optimize its performance. A novel decoding algorithm based on the alternating directions method of multipliers is derived to reconstruct signals from a limited number of received descriptions. Simulations are performed to assess the performance of CS-GQ against other methods in presence of packet losses. The proposed method is successful at providing robust coding of CS measurements and outperforms other schemes for the considered test metrics.

A linear programming approach to sparse linear regression with quantized data

“…, m, which makes the ∞ -norm description more suitable than the 2 one, as illustrated in [11], [12]. In particular, the ∞ -norm supports the consistency principle: the measurements obtained from the recovered signal lie in the same quantization intervals of the observed measurements, as considered in [13], [14], [11], [12].…”

“…Exploiting the zero duality gap between primal and dual in LP problems [29], if (12) has solution that originates a positive penalty, the penalty is positive also for (11), which is our final aim. From this point, the thesis can be obtained following the same procedure used in [10, pages 518-519], since problem (12) is analogous to problem ( 21) in [10], with different constants. We omit the details for brevity.…”

Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices

“…The probability P sw (δ) is of fundamental importance, since it determines the performance of CS. In the next section, an approach for exactly calculating (9) for Gaussian matrices is proposed.…”

Sparse linear regression with compressed and low-precision data via concave quadratic programming

“…The choice p = 2 bounds the mean energy of the error, hence BPDN 2 is tolerant to possible outliers. The case p = ∞, instead, is considered to deal with quantized or low-precision data in [7,14,26,4]. When y is quantized, a bound on each component is given, and no outliers occur.…”