Thresholding-based reconstruction of compressed correlated signals

TL;DR

This paper introduces a thresholding-based joint reconstruction algorithm for correlated signals acquired via compressed sensing, exploiting geometrical transformations to improve support recovery and reconstruction quality.

Contribution

It proposes a novel correlation model and a simple thresholding decoder that significantly outperforms independent decoding methods.

Findings

Outperforms independent decoding in support recovery

Achieves higher reconstruction quality

Theoretically and experimentally validated

Abstract

We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measurements per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear measurements and sends it to a joint decoder for reconstruction. We propose a novel joint reconstruction algorithm that exploits correlation among underlying signals. Our correlation model considers geometrical transformations between the supports of the different signals. The proposed joint decoder estimates the correlation and reconstructs the signals using a simple thresholding algorithm. We give both theoretical and experimental evidence to show that our method largely outperforms independent decoding in terms of support recovery and reconstruction quality.