Compressed sensing in the presence of speckle noise

TL;DR

This paper investigates the theoretical possibility of recovering structured signals from fewer measurements than their ambient dimension in the presence of speckle noise, a common challenge in imaging systems, and demonstrates the effectiveness of the proposed methods through simulations.

Contribution

It provides the first theoretical analysis showing that undersampled measurements can accurately recover structured signals affected by speckle noise.

Findings

Successful signal recovery with fewer measurements than ambient dimension.

Effective denoising of speckle noise in undersampled measurements.

Simulation results validate the theoretical findings.

Abstract

The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The current acquisition technology oversamples signals and converts the problem into a denoising problem with multiplicative noise. However, this paper explores the possibility of reducing the number of measurements below the ambient dimension of the signal. The sophistications that appear in the study of multiplicative noises have so far impeded theoretical analysis of such problems. This paper aims to present the first theoretical result regarding the recovery of signals from their undersampled measurements under the speckle noise. It is shown that if the signal class is structured, in the sense that the signals can be compressed efficiently, then one can obtain accurate estimates of the signal from fewer measurements than the ambient dimension. We demonstrate the effectiveness of the methods we propose through simulation results.