Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels

TL;DR

This paper develops a power-efficient sensing matrix design for sparse Gaussian linear dimensionality reduction over noisy channels, optimizing MSE performance in single- and multi-terminal systems with practical algorithms.

Contribution

It introduces a three-stage optimization scheme combining SDR, low-rank approximation, and power rescaling, with closed-form solutions under certain conditions, and proposes a stochastic method for complexity reduction.

Findings

Proposed scheme outperforms existing methods in MSE performance.

Closed-form solutions derived for specific conditions.

Stochastic optimization offers a practical alternative with good performance.

Abstract

In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single-- and multiple--terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closed-form solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.