Research On Image Restoration Algorithms

The presence of image degradation, such as noise and blurring, is unavoidable. It may be introduced by the image formation process, image recording, image scanning, image transfer, image showing, etc. However, in many applications, the clear images are needed. The image restoration technique, restoring the original image from the degraded image, is coming to resolve this problem, which is the fundamental problem of image processing, pattern recognition, and computer vision. So, image restoration is widely used in astronomy, remote sensing, medical image, etc.The traditional image restoration methods rest on the image filter. Since image edges contain lots of image information, and human being is sensitive to these high frequency parts, image filter technique need deblurring image and suppressing the noise, while preserving image edges. However, both image edges and the noise are high frequency part of the image. So, image smoothing is in contradiction to with preserving image edges during image restoration. The traditional filter methods can not deal with this. In recent years, some image processing techniques, such as variational PDEs (Partial Differential Equations) methods, neural network, wavelet analysis, and graph cut techique, are emerging to solve this contradiction.This dissertation is mainly focus on the image deblurring and de-noising problem, and total variation restoration model. In this dissertation, we research into the image restoration models and algorithms based on neural network; analyze the relationship between wavelet image de-noising method and nonlinear filter de-noising method; study the computation methods of total variation de-noising model using graph cut technique. The main original contributions of this dissertation are summarized as follows:(1) The study on image restoration algorithm based on neural network â—†Two image restoration models and algorithms based on a modified Hopfield neural network and variational PDEs are proposed. Two variational PDEs as the regualarization terms are proposed to the image restoration model based on the modified Hopfield neural network. One is based on a harmonic model and the other is based on a total variation model. The performance of these regularization terms is analyzed from the viewpoint of nonlinear diffusion. It can be shown that the two proposed restoration models have superior edge preserving performance than the traditional restoration model. Two algorithms have been proposed based on the harmonic model and the total variation model.â—†A fast neural network restoration algorithm based on MHNN (modified Hopfield neural network) of continuous state change is presented. This algorithm uses the MHNN based on continuous state change, and maximal energy descent in the update rule. The convergence of the algorithm is proofed. Experimental results show that the algorithm could converge to a stable point with higher speed, and give more precise restoration results.â—†Two improved restoration algorithms based on the harmonic model and MHNN are given. One is a fast sequential algorithm. The other is a parallel algorithm based on MHNN of continuous state change. Experiment results show that the fast algorithm can restore the degraded image while preserving the edge in a fast speed, and that the parallel algorithm based on the harmonic model is superior to the existing parallel algorithms based on Laplace operator in the performance of preserving image edges.(2) The study on image restoration algorithm based on wavelet analysisâ—†Studying the relationship between nonlinear diffusion and wavelet shrinkage denoising method. We study the relations and differences between nonlinear diffusion and 2D Haar wavelet shrinkage de-noising, explain the characteristic of nonlinear diffusion in wavelet shrinkage framework, and show that nonlinear diffusion is superior to Haar wavelet shrinkage.â—†A hybrid de-noising algorithm, based on 2D Haar wavelet shrinkage and total variation (TV) diffusion, is proposed. The hybrid algorithm is a tradeoff between restoration quality of images and computing complexity. This algorithm applies TV diffusion to low frequency part of image decomposed by Haar wavelet, and shrinks the wavelet coefficient. Some experiment results show that this hybrid algorithm preserves the advantages of these two image de-noising methods, and has the better general performance.(3) The study on image restoration algorithm based on graph cut techniqueâ—†A TV image de-noising algorithm based on graph cut is proposed. In this algorithm, the minimum of the total variation image de-noising energy function is transformed to a minimum cut of a certain graph. Then, some maximum flow/minimum cut algorithms could solve this problem, and get the global minimum of the TV energy function. In addition, an adaptive method of the proportion coefficient is given. Experiment results show that the algorithm proposed could avoid the staircase effect occurred in some classical total variation minimization methods, and has the better restored effect.â—†A TV image de-noising method based on move space is presented. In this method, the minimum problem of energy function based on TV model is mapped to a the optimal label problem in move space, which could be solved by minmum cut/maximum flow algorithm. This method avoids the computing trouble occurred in classical minimization methods. In addition, the regulative parameter can be adaptively set according to the local character of the noised image. In this way, the minimization method proposed avoids the staircase effect and over smoothing occurred in some classical total variation minimization methods. Experimental results show that the proposed algorithm is preferable to classical total variation minimization method in image denoising performance.