Compressed Sensing with Probability-based Prior Information

TL;DR

This paper introduces a novel compressed sensing framework that leverages probability-based prior information to design sensing matrices and improve sparse recovery accuracy, demonstrated through simulations and real-world applications.

Contribution

It proposes a new sensing matrix design and a probability-driven recovery algorithm that utilize prior probabilities to enhance compressed sensing performance.

Findings

Outperforms existing CS algorithms in simulations

Achieves lower computational complexity in sensing matrix design

Improves recovery accuracy in surveillance video applications

Abstract

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the dictionary being used, a diagonal weighted matrix is obtained and then the sensing matrix is designed by minimizing a weighted function such that the Gram of the equivalent dictionary is as close to the Gram of dictionary as possible. An analytical solution for the corresponding sensing matrix is derived which leads to low computational complexity. We also exploit this prior information through the sparse recovery stage and propose a probability-driven orthogonal matching pursuit algorithm that improves the accuracy of the recovery. Simulations for synthetic data and application scenarios of surveillance video are carried out to compare the performance of the proposed methods with some existing algorithms. The results reveal that the proposed CS system outperforms existing CS systems.