A Research On Wavelet Networks Related Issues

Due to limitations of devices and the impact of environment, the image inevitablyloses some information in the process of the image formation and transmission. Imagerestoration processing is aimed at improving the image quality and it is one of the earliestand most important problems in image processing, which can trace back to the1960s. Itplays an improtant part in various areas of applied sciences such as medical, astronomicalimaging, film restoration, etc.Digital image restoration/reconstrction is a linear inverse problem of the imagedegradation, which estimates the process of the image degradation and tries to find miss-ing information of image by solving a mathematical model, also it is an important prepro-cessing step for other image processing tasks.Firstly, we introduce the theoretical basis of image restoration problems and the mod-e for image restoration problems while we discuss the ill-posedness of image restorationproblems and several classic regularization methods. Of course, we give a few evaluationcriterions, including objective and subjective criterions.In image deblurring, the problem is not only large scale but also involves dense ma-trix data. This motivate we search a simpler method to solve this problem. We considerthe class of iterative shrinkage algorithm(ISTA). This class of methods can be viewed asan extension of classical gradient algorithm and it is very simple, which each iterativeinvolves relatively cheap matrix-vector multiplications. But such methods converge veryslowly. In fact, it shares a sublinear global rate of convergence. In this paper, we intro-duce two accelerated algorithms TWIST and FISTA of this class methods. We also givespecific forms and convergence analysis of this two accelerated algorithms for both l1regularization or total-variation regularization.Finally, we introduce the decoupling model of deblurring and denoising, state its ad-vantages and propose a split fast iterative shrinkage/thresholding algorithm based on thismodel. In the forth chapter, we illustrate the performance of the new algorithm to solvethe problems of image restoration for both l1regularization or total-variation regulariza- tion. The proposed method is quite fast than other methods in the literature while thesignal to noise ratio values remain at the same level.