Online Learning Sensing Matrix and Sparsifying Dictionary Simultaneously for Compressive Sensing

TL;DR

This paper introduces an online algorithm for jointly learning the sensing matrix and sparsifying dictionary in compressive sensing, improving signal recovery accuracy on large datasets.

Contribution

It proposes a novel online method that optimizes sensing matrices and dictionaries simultaneously, enhancing performance over existing approaches.

Findings

Improved signal recovery accuracy on natural images.

Effective online algorithm demonstrated through simulations.

Outperforms existing methods in compressive sensing tasks.

Abstract

This paper considers the problem of simultaneously learning the Sensing Matrix and Sparsifying Dictionary (SMSD) on a large training dataset. To address the formulated joint learning problem, we propose an online algorithm that consists of a closed-form solution for optimizing the sensing matrix with a fixed sparsifying dictionary and a stochastic method for learning the sparsifying dictionary on a large dataset when the sensing matrix is given. Benefiting from training on a large dataset, the obtained compressive sensing (CS) system by the proposed algorithm yields a much better performance in terms of signal recovery accuracy than the existing ones. The simulation results on natural images demonstrate the effectiveness of the suggested online algorithm compared with the existing methods.