A Double Recursion Algorithm to Image Restoration from Random Limited Frequency Data

摘要

One of the main tasks in image restoration is to catch the picture characteristics such as interfaces and textures from incomplete noisy frequency data. For the cost functional with data matching term in frequency domain and the total variation together with Frobenius norm penalty terms in spatial domain, the properties of the minimizer of cost functional and the error estimates on the regularizing solution are established. Then we propose an algorithm with double recursion to restore piecewise smooth image. The Bregman iteration with lagged diffusivity fixed point method is used to solve the corresponding nonlinear Euler-Lagrange equation. By implementing recursion algorithms a few times, the satisfactory reconstructions can be obtained using random band sampling data. Numerical implementations demonstrate the validity of our proposed algorithm with good edge-preservations.