Local sparsity and recovery of fusion frames structured signals

TL;DR

This paper introduces a fusion frame-based compressed sensing framework that splits complex signals into local parts measured by low-quality sensors, enabling accurate, robust, and efficient signal recovery.

Contribution

It presents a novel fusion frame approach for compressed sensing that enhances robustness and recovery performance by local splitting and fusion of signals.

Findings

Improved signal recovery accuracy over traditional methods.

Enhanced robustness to noise with larger fusion frames.

Low computational complexity with stronger performance.

Abstract

The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in fusion frames, we introduce a compressed sensing framework in which we split the dense information into sub-channel or local pieces and then fuse the local estimations. Each piece of information is measured by potentially low quality sensors, modeled by linear matrices and recovered via compressed sensing -- when necessary. Finally, by a fusion process within the fusion frames, we are able to recover accurately the original signal. Using our new method, we show, and illustrate on simple numerical examples, that it is possible, and sometimes necessary, to split a signal via local projections and / or filtering for accurate, stable, and robust estimation. In particular, we show that by increasing the size of the fusion frame, a certain robustness to noise can also be achieved. While the computational complexity remains relatively low, we achieve stronger recovery performance compared to usual single-device compressed sensing systems.