有效的半张量压缩感知测量矩阵优化方法

Semi-Tensor Product Compressed Sensing (STP-CS) breaks through the limitation of dimension matching between the measurement matrix and the measured data in the traditional compressed sensing (CS), and it greatly reduces the storage space of the measurement matrix. However, the dimension reduction of the measurement matrix leads to the reduction in recovery accuracy. Therefore, in order to improve the recovery effect of the STP-CS, this paper proposes an effective optimization method of the measurement matrix for STP-CS based on the gradient descent, which can reduce the correlation coefficients of the final measurement matrix by optimizing the initial low-dimensional measurement matrix according to the properties of the semi-tensor product and the measurement matrix in STP-CS, thus improving the reconstruction performance of STP-CS. The simulation experiments are conducted to verify the effectiveness of the optimization method proposed in this paper and the experimental results demonstrate that it improves the recovery effect of STP-CS and its recovery effect is very stable. In addition, compared with the optimization method of the measurement matrix in the traditional CS, the proposed optimization method of the measurement matrix in STP-CS can save the storage space, reduce the optimization time and the computational complexity of the measurement matrix optimization, and it has more obvious advantages especially when compressing the high-dimensional data.