Improved Recovery of Analysis Sparse Vectors in Presence of Prior Information

TL;DR

This paper presents a method for improving the recovery of analysis-sparse signals by optimally tuning weights in a weighted $ ext{l}_1$ analysis optimization, leveraging prior support information and statistical dimension bounds.

Contribution

It introduces a novel weight tuning strategy based on statistical dimension bounds to enhance analysis-sparse signal recovery with prior support information.

Findings

Weighted $ ext{l}_1$ analysis outperforms standard methods.

Tuned weights reduce the number of measurements needed.

Numerical simulations validate the effectiveness of the approach.

Abstract

In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning the weights in a weighted $\ell_1$ analysis optimization problem. Indeed, we try to set the weights such that the method succeeds with minimum number of measurements. For this purpose, we exploit the upper-bound on the statistical dimension of a certain cone to determine the weights. Our numerical simulations confirm that the introduced method with tuned weights outperforms the standard $\ell_1$ analysis technique.