Two-Part Reconstruction in Compressed Sensing

TL;DR

This paper introduces a two-part reconstruction framework in compressed sensing that combines algorithms to speed up recovery without losing accuracy, extending previous work to noisy and 1-bit settings with promising results.

Contribution

It extends the Sudocodes algorithm to be robust against noise and demonstrates improved speed and quality in 1-bit compressed sensing.

Findings

Reduced run-time in 1-bit CS

Improved reconstruction quality

Robustness to measurement noise

Abstract

Two-part reconstruction is a framework for signal recovery in compressed sensing (CS), in which the advantages of two different algorithms are combined. Our framework allows to accelerate the reconstruction procedure without compromising the reconstruction quality. To illustrate the efficacy of our two-part approach, we extend the author's previous Sudocodes algorithm and make it robust to measurement noise. In a 1-bit CS setting, promising numerical results indicate that our algorithm offers both a reduction in run-time and improvement in reconstruction quality.