Optimization algorithm for measurement matrix based on fractional order Duffing system

In order to improve the reconstruction accuracy of images in compressed sensing, a quantitative matrix optimization algorithm based on fractional order Duffing system is proposed. Firstly, the measurement matrix is constructed by using the pseudo-random sequence generated by fractional Duffing system. Then, the Gram matrix of the sensor matrix is generated by taking the identity matrix as the sparse basis and the measurement matrix, and the normalization constraint of all elements of the Gram matrix is introduced into the metric, which is accomplished by gradient descent. Finally, in view of the occurrence of local low points in the optimization process of two-dimensional compressed sensing measurement matrix, an algorithm is proposed to find the relatively optimal measurement matrix to assist the previous measurement matrix optimization algorithm. The experimental simulation results show that the proposed algorithm can improve the accuracy of image reconstruction in different degrees.