Application of Measurement Matrix Based on Linear Representation of Diagonal Matrix in Image Restoration

In recent years, compressed sensing theory has been widely used in signal processing and image restoration. As an important part of compressed sensing, the performance of measurement matrix directly affects the efficiency and accuracy of image restoration. The common measurement matrix can not take a good balance between the two. By utilizing the linear representation theory of orthogonal basis, this essay proposes a new method, which introduces diagonal matrix with non-zero elements on main diagonal and the pseudo-random number. The simulation result shows that the new matrix is superior to others. Especially when the compression ratio is less than 0.5, the number of measurements is reduced by about 40% and the Peak Signal to Noise Ratio is increased by at least 2.2dB.