A new robust compressed sensing mathematical model applied to image restoration

In this paper, we first conducted a detailed analysis of the perturbation phenomenon of the sensing matrix, and then, through statistical learning theory, we established a robust optimization and reconstruction mathematical model of compressed sensing based on the perturbation of the sensing matrix. Finally, we carried out a detailed analysis of the optimization of the model. The model is resistant to disturbance uncertainty. As an extension of the standard mean square error boundary constraint, it introduces the distortion parameters caused by sampling and other factors to determine the relationship between the mean square error of the estimated signal and the sparse measure. The robust compressed sensing optimization algorithm based on disturbance established in this paper belongs to the category of convex optimization. Most importantly, the proposed model is proved to be reasonable and mathematical. Finally, we apply the mathematical model of compressed sensing to image similarity comparison, and the experimental results show that the mathematical model has a good matching effect in the field of image similarity, which meets our requirements.