Based On Image Restoration Technology Research Of Numerical Algebra

During the relative motion, atmospheric interference, defocusing, noise and so many other factors existing, an image quality in the processing of acquisition, transfer and record keeping would be degraded inevitably. How to recover the original image from a degraded image are attracting more and more attention from people. After many scholars research, there has been a lot of restoration algorithms. At present, the recovery algorithm based on regularization is the most effective algorithm.On the basis of the numerical algebra, the dissertation focusing on the recovery method based on the total variation regularization. It’s not only overcomes some of the shortcoming of the Tikhonov regularization. But also it can preserve the edge information. And the restoration effect is better than mostly classical iterative algorithms. Based on this, the mainly content of this dissertation are as follows:Firstly, according to the image degradation system, we establish the degradation model, then evolutes the degradation model to the solution of linear systems which is based on the numerical algebra, and descript some classical iterative solving methods briefly.Then, we descript the total variation which bases on the Fourier transform (Fast Total Variation deconvolution:FTVd) principle and the restoration algorithm in details. At the same time, from the engineering application point of view, we verify its shortcomings by theoretical analysis and numerical experiments.Finally, according to the augmented Lagrange method of optimization theory, we present a modify FTVd (M_FTVd) algorithm. This algorithm overcomes the shortcomings of the FTVd algorithm. At the same time, the image effects and the convergence time of the M_FTVd algorithm are significantly than FTVd algorithm was proved through theoretical analysis and numerical experiments.