Robust CS reconstruction based on appropriate minimization norm

TL;DR

This paper proposes a noise-robust compressive sensing algorithm that adapts the minimization norm to improve signal reconstruction accuracy under various noise types, including Cauchy and Cubic Gaussian noise.

Contribution

It introduces the use of the l3 minimization norm for better reconstruction in non-Gaussian noise environments, expanding beyond traditional l1 and l2 norms.

Findings

l3 norm improves reconstruction with Cauchy noise

Adaptive norm selection enhances robustness

Demonstrated effectiveness on example signals

Abstract

Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly used l1 and l2 norms, provide good results in case of Laplace and Gaussian noise. However, when the signal is corrupted by Cauchy or Cubic Gaussian noise, these norms fail to provide accurate reconstruction. Therefore, in order to achieve accurate reconstruction, the application of l3 minimization norm is analyzed. The efficiency of algorithm will be demonstrated on examples.