Research And Application Of Regularization In Image Restoration

Image restoration is one of the essential topics in image processing, which can greatly improve image quality. The key for this issue is to model the degradation processing in mathematical form, then solve this inverse problem to get a restoring model and an estimation of original image. Effective methods that can tackle the ill-posed problems are the so-called regularization methods during the inverse process. This thesis introduces and analyses in detail the research and application of regularization in image restoration, the main contributions and creativities are listed as follows:Firstly, on the basis of the regularization technique for dealing with ill-posed problems, starting from the mathematical theories about regularization, analyzing the degraded model and the ill-posed character of image restoration, this paper mainly discusses the regularized parameter and regularized item, and the solution approaches and fast algorithms are also summarized, therefore perfects the essential theories about regularization in image restoration.Secondly, to perfect the known restoring models, a new space-adaptive regularization model of image restoration is constructed by redesigning regularized parameter and regularized item. By contriving appropriate algorithms in the computations, the regularized parameter can automatically correct to the appropriate value due to its adaptive character, meanwhile, the adaptive effect is developed with a weight matrix included in the regularized item. Simulation results show that the ringing artifacts around the image are reduced, the main information is preserved, and the Peak Signal to Noise Ratio (PSNR) is higher than the known methods.Thirdly, two new image restoration methods are proposed based on regularization idea from traditional linear algebra approach. On one hand, from the technique of constrained least squares and limited energy of additive noise, an effective restored approach by adopting regularization method to overcoming ill-posed problem, solving an equation with a single variable, and using space iterative algorithm is proposed; On the other hand, aiming at the restoration of blurred image, another effective restoration approach based on least-square algorithm is also proposed in this paper. This method firstly adopts increment iterative algorithm to improve convergence and meanwhile applies regularization technique to overcome ill-posed problem. In the computations, the regularized parameter has its adaptive character, which can be determined in terms of the restored image at each iteration step therefore automatically correct to the appropriate value. Numerical results show that these methods can effectively restore original image, and the objective standard evaluation and subjective visual effect are improved significantly.