An improved PCG algorithm for image restoration and reconstruction

To deal with the shortcoming of the preconditioning conjugate gradient (PCG) method with Tikhonov regularization in which the blurred image is extended with a zeros extension matrix. With the careful analysis of the PCG method with Tikhonov regularization under zero boundary condition, a new extension matrix for the blurred image was proposed. It could decrease the matrix vector multiplication computational error and modify the initial gradient. The improved algorithm is in accord with the real image blurring process and increases the quality of recovered image. Experiments show that, compared with the state-of-the-art algorithms of IST, TwIST and SALSA which solve the total-variation (TV) regularization, the proposed algorithm performs favorably.