A fast image recovery algorithm based on splitting deblurring and denoising

In this paper, we employ a popular splitting strategy to design a fast iterative algorithm for image restoration. We divide the algorithm into two steps, i.e., deblurring step and denoising step. In the deblurring step, Fourier transform is employed for image deblurring under the periodic boundary condition. In the denoising step, we use a simple and fast method, called fast iterative shrinkage/thresholding algorithm (FISTA), to reduce image noise. In addition, we also give the convergence analysis for the proposed method. Visual and quantitative results demonstrate the proposed algorithm, applied to l1l1 regularization model and total-variation (TV) regularization model, is a faster algorithm and keeps image details well.