Non-blind image deconvolution using sampling without replacement

Image degradations can be modeled as a process of linear systems which are usually denoted by convolution. Deconvolution refers to a reverse operation of the linear system in which an original image is convolved with a blur kernel, which is also known as a point spread function (PSF) of the linear system. If the blur kernel, which can represent linear degradations such as an out-of-focus blur or motion blurs due to the shake of a camera, is known, we call this ill-posed problem the non-blind deconvolution problem. In this paper, we propose a non-blind deconvolution method using a convex optimization method in which a non-derivative approach is used to solve the ill-posed problem. The proposed method minimizes the objective function using the stochastic process in which the random variable selects the coordinate. The objective function is minimized along the selected coordinate direction at each iteration. If several coordinate directions are picked simultaneously, the cost can be decreased independently along each coordinate direction.