Linearized Bregman Iterations for Frame-Based Image Deblurring

Real images usually have sparse approximations under some tight frame systems derived from either framelets, over sampled discrete (window) cosine or Fourier transform. In this paper, we propose a method for image deblurring in tight frame domains. It is reduced to finding a sparse solution of a system of linear equations whose coefficients matrix is rectangular. Then, a modified version of the linearized Bregman iteration proposed and analyzed in [10, 11, 43, 50] can be applied. Numerical examples show that the method is very simple to implement, robust to noise and effective for image deblurring.