A robust and efficient algorithm for distributed compressed sensing

In this paper we present a new iterative greedy algorithm for distributed compressed sensing (DCS) problem based on the backtracking technique, which can reconstruct several input signals simultaneously by processing column by column of the compressed signals, even when the measurements are contaminated with noise and without any prior information of their sparseness. This makes it a promising candidate for many practical applications when the number of non-zero (significant) coefficients of a signal is not available. Our algorithm can provide a fast runtime while also offers comparably theoretical guarantees as the best optimization-based approach in both the noiseless and noisy regime. Numerical experiments are performed to demonstrate the validity and high performance of the proposed algorithm.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We define two joint sparse models to model different connections between signals. ► We propose a fast and robust iterative greedy algorithm for joint signal recovery. ► It can simultaneously reconstruct multi-signal without requiring signal’s sparseness. ► It can offer nearly best theoretical guarantees in both noiseless and noisy regime.