Domain decomposition method for image deblurring

As a fundamental problem in image processing, image deblurring has still attracted a lot of research attention. Due to the large computational cost, especially for high-resolution images, it becomes challenging to solve the deblurring minimization problem and the underlying partial differential equations. The domain decomposition method (DD), as one of the most efficient algorithms for solving large scale problems, had not been applied directly to image deblurring because of the global characteristic of the blur operator. In this paper, in order to avoid separating the blur operator, we propose an algorithm for directly solving the total variational based minimization problems with DD. Various numerical experiments and comparisons demonstrate that the larger the image size is, the more efficient the proposed method is in saving running time. The parallelization has also been realized by using the parallel computing toolbox of MATLAB.