Bound Constrained Regularization Problems For Image Processing

Image restoration is an important branch of image processing. Generally, with use of some knowledge of image degenerate, it is need to analysis degenerate reason, establish mathematical model, and deduce reversely. In this paper, we investigate image deblurring problem which is one of main image restoration problems. When blurring date z, Operator K and Varianceσ~2 of noise n are known, we want to restore u from the model z = Ku+n. Specially,if K is identity operator, the problem is so-called image denoising problem. These problems are ill-posed. First of all, because the L~2-based denoising model could not keeps the edge of image, and the L~1-based Total Variation denoising model may produce the staircasing effect, in the thesis, we propose an adaptive image denoising model which based on L~p(1≤p≤2) norm, and investigate the adaptive function. Secondly, supposing U is provided which is a upper boundary of u , we use the U as a Constrain, combine the TV Regularization, propose a Bound Constrained Regularization model, and we use the Primal-Dual method to solve the BC model. Our denoising, deblurring models can remove the noise while preserving details of edge, and reduce staircase effect. The image which is restored by our models have more improvement than the other models for signal-to-noise ration.