Image Restoration: Model, Bayesian Inference And Iteration Algorithms Research

The presence image degradation is unavoidable due to the atmospheric turbulence, relative motion, defocus, imaging device limitations, noise and other factors. However, in many applications, the high-definition and quality images are needed . The image restoration technique is to restore original image for degraded image and is significant. It is the fundamental problem of image processing, pattern recognition and machine vision and is widely used in astronomy, remote sensing, medical image and military, etc.This dissertation focuses on the research on image restoration, including image models, the Bayesian rules for image estimation and fast iteration algorithms. Firstly, we research on image wavelet domain models and spatial Markov random field (MRF) models, and proposed image restoration method based maximum a posterior (MAP) estimation and variational Bayesian principle. We then discuss the iteration algorithms for image restoration and obtain the conclusion that the multi-step iteration algorithms are fast convergence. At last, we generalize the proposed models and inference method to multi-frame images super-resolution restoration problems and give conclusions and expectation. Several research aspects are presented in this dissertation, they are:The basic theory and method are introduced The ordinary degradation model of imaging system and several point spread function (PSF) expression are depicted. The research status of image spatial MRF models and multi-scale transform domain models are discussed. At the same time, we review several classical image restoration methods and emphasize the Bayesian method. At last, some objective and subjective criterions for evaluate image quality are proposed.We research on the wavelet domain image restoration methods in detail. The basic property of image wavelet coefficient and classical wavelet domain statistical models are discussed. We proposed a double level model of image wavelet coefficient. For this model, we assumed that wavelet coefficients obey zero mean local Gauss distributions and estimate local Gauss variance by Bayesian method. Then, A wavelet domain image restoration algorithm is proposed based on this prior distribution model.The MAP estimation for image restoration is point estimation and we haven't efficient methods to estimate model parameters. To this limitation, this dissertation proposed a joint image restoration and parameters estimation method based on wavelet domain variational Bayesian theory. We can calculate the posterior density function of original image through variational Bayesian method and the function mean is regarded as restoration image. Through this method, we avoid the lack of MAP estimation method and obtain the good restoration results.Spatial MRF theory is discussed systematically. We proposed an image restoration algorithm based on local double level MRF models and expectation maximization (EM) algorithm. This algorithm can be thought as empirical Bayesian method and the hyper-parameters are eliminated by intergrating. Then, the estimated value of original image is obtained by MAP. The restoring image quality by this method is poorer than wavelet domain image restoration method that has been discussed in last chapter. However, it is better than wavelet method according to computational complexity. At the same time, a blind image restoration algorithm is proposed base MAP estimation. We characterize the statistical distribution property of original image and PSF by using different priori models and gain the estimated results of original image and PSF through alternating minimization (AM) algorithm.At present, the traditional low-order MRF models can not characterize the image high-order statistical properties and the model parameters are gained by empirical form. In this dissertation, we adopted a new machine learning method-score matching and get a group of parameters of high-order MRF models by learning from training image data. We demonstrated the capabilities of the learning MRF models by applying them to image denoising according to Bayesian rule. Experiments show that our denoising algorithm can produce excellent results in the Peak Signal-to-Noise Ratios (PSNR) and subjective visual effect. Thus, our learning method is effective.We depicted the common image restoration iteration algorithms, including AM algorithm, majorization-minimization (MM) algorithm and EM algorithm. These algorithms are called as single-step iteration algorithms as the current iteration solutions of these algorithms only depend on previous one step solution. We find that the convergence rate of these iteration algorithms is slow through some restoration experiments, such as total variation and wavelet domain image restoration. For this reason, multi-step iteration restoration algorithms are proposed. The multi-step iteration algorithms have fast convergence rate because the current solutions of these algorithms depend on more previous solutions. At same time, the computational complexity of the multi-step algorithms is same as the single-step algorithms in each iteration step and can achieve convergence using less iteration numbers.The proposed image models and inference algorithms are generalized to multi-frame images super-resolution (SR) restoration. We proposed a wavelet domain SR image restoration method and jointly estimate high-resolution (HR) image and motion parameters based on variatonal Bayesian theory. And at same time, a Simultaneous image SR and registration algorithm are presented using Gauss-Newton algorithm. According to this algorithm, we consider unknown HR image and motion parameters vector as one whole and simultaneous estimation using Gauss-Newton algorithm. The merit of this algorithm is that it is robust to initial motion parameters, so this algorithm can recover the HR image and simultaneously estimate high-precision motion parameters vector.