Research Of Image Restoration Based On Convex Optimization Method

Video and Image have become an important means of acquiring, transmitting information. And widely used in military, astronomy, aviation, medical, networking, and other fields. Because of the physical material and external environment, the equipment of image acquisition, transmission, storage, will introduce noise, pixels-missing, blurring. For keeping the integrity of image information, image restoration techniques will be need as a tools, serve the subsequent advanced image processing.Image Restoration is very fundamental and important. In this paper, we mainly do some research on image restoration based on convex optimization method.1) We introduce the convex optimization model and some basic concepts in engineering. This is applied to compressive sensing and image restoration. And study the gradient descent method, iterative soft threshold method, and primal-dual method in detail.2) We introduce the TV prior model for image restoration. The advantage of TV is that it can exploit image blocky structure and preserve edges, though it is generally challenging to solve TV model efficiently in practice because of its nonsmooth, we can make use of an approximal model, or iterative shrinkage threshold algorithm.3) We study a sparsity prior model for image restoration. It can keep the detail of image, like wavelet, curvelet. The curvelet prior can avoid the drawback of wavelet, and it is much more successful in recovering long elongated structures and the smooth background structures.4) We study a primal dual algorithm, it can be very flexible to solve total variation or sparse regularization for image restoration. Base on them, we proposed a primal-dual algorithm for hybrid of curvelet and TV prior model. and it performs well when it is applied to denosing, inpainting. So we can conclude that the new mode for image restoration is feasible.