No abstract

This paper deals with designing sensing matrix for compressive sensing systems. Traditionally, the optimal sensing matrix is designed so that the Gram of the equivalent dictionary is as close as possible to a target Gram with small mutual coherence. A novel design strategy is proposed, in which, unlike the traditional approaches, the measure considers of mutual coherence behavior of the equivalent dictionary as well as sparse representation errors of the signals. The optimal sensing matrix is defined as the one that minimizes this measure and hence is expected to be more robust against sparse representation errors. A closed-form solution is derived for the optimal sensing matrix with a given target Gram. An alternating minimization-based algorithm is also proposed for addressing the same problem with the target Gram searched within a set of relaxed equiangular tight frame Grams. The experiments are carried out and the results show that the sensing matrix obtained using the proposed approach outperforms those existing ones using a fixed dictionary in terms of signal reconstruction accuracy for synthetic data and peak signal-to-noise ratio for real images.

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.

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This study deals with the issue of designing the sensing matrix for a compressed sensing (CS) system assuming that the dictionary is given. Traditionally, the measurement of small mutual coherence is considered to design the optimal sensing matrix so that the Gram of the equivalent dictionary is as close to the target Gram as possible, where the equivalent dictionary is not normalised. In other words, these algorithms are designed to solve the CS problem using an optimisation stage followed by normalisation. To achieve a global solution, a novel strategy of the sensing matrix design is proposed by using a gradient‐based method, in which the measure of real mutual coherence for the equivalent dictionary is considered. According to this approach, a minimised objective function based on alternating minimisation is also developed through searching the target Gram within a set of relaxed equiangular tight frames. Some experiments are done to compare the performance of the newly designed sensing matrix with the existing ones under the condition that the dictionary is fixed. For the simulations of synthetic data and real image, the proposed approach provides better signal reconstruction accuracy.