Design of Compressed Sensing System With Probability-Based Prior Information

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.

Measurement-Driven Framework With Simultaneous Sensing Matrix and Dictionary Optimization for Compressed Sensing

“…(16) makes the sparse coefficients totally associate with the measurements and the measure procedure (according to sensing matrix and dictionary ). Remark 2: It should be declared that (14) is the process concerning signal reconstruction, this is exactly the reason why we choose (16) to update sparse coefficients in the system design strategy. Make this updating procedure fully connected with the signal reconstruction, then utilize the obtained sparse coefficients to optimize sensing matrix and dictionary, so that and will be implicitly adapted to the reconstruction accuracy.…”

“…should be included in the design model naturally. Once again, in our measurement-driven framework, the sparse coefficients are updated by (16), so 1 ( ) is just a cost function of , and S is viewed as a constant matrix when minimizing 1 ( ). This is totally different from the traditional dictionary learning problem (2).…”

“…to design the CS system for preferable performance. Regarding this penalty term, S is also treated as a constant matrix which is calculated with an independent step by (16). Based on the discussions above, the following multiobjective cost function for simultaneously optimizing sensing matrix and dictionary is proposed:…”

“…A two-stage alternating minimization procedure is usually adopted. The first stage is sparse coding, aiming at finding the (column) sparse matrix S with a given , i.e., This problem can be solved by orthogonal matching pursuit (OMP) based techniques [14]- [16]. Many algorithms differentiate each other mainly in the second stage named dictionary updating [12], [13], that is to update with the obtained S fixed.…”

“…Similar with (3) and (4), such problem can also be addressed using the greedy algorithms, such as OMP based techniques [14]- [16]. The estimated signal is simply obtained with x = s. A key notion for signal reconstruction is the restricted isometry property (RIP) [1], [3].…”