Linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization

Non-blind motion deblurring problems are highly ill-posed and so it is quite difficult to find the original sharp and clean image. To handle ill-posedness of the motion deblurring problem, we use nonlocal total variation (abbreviated as TV) regularization approaches. Nonlocal TV can restore periodic textures and local geometric information better than local TV. But, since nonlocal TV requires weighted difference between pixels in the whole image, it demands much more computational resources than local TV. By using the linearization of the fidelity term and the proximal function, our proposed algorithm does not require any inversion of blurring operator and nonlocal operator. Therefore, the proposed algorithm is very efficient for motion deblurring problems. We compare the numerical performance of our proposed algorithm with that of several state-of-the-art algorithms for deblurring problems. Our numerical results show that the proposed method is faster and more robust than state-of-the-art algorithms on motion deblurring problems.