Research On The Applications Of Variational Model And Sparse And Redundant Representation In Image Restoration

Image restoration is to revert the original image of the real scene about the objective world from the observed image based on the prior knowledge of degradation model and image itself. It is an important prior technology to guarantee the right understanding of the information contained in the image and the effectiveness of the subsequent image processes. The construction of a variational restoration model is an effective approach to solve the problem of image restoration. When the image degradation model is known or estimated in advance, the prior knowledge of image itself is directly related to the accuracy of the variational restoration model and thus determines the image restoration performance. The piecewise smooth and the sparsity of the transform coefficients are the two important characteristics about the image signal. They help to design the regularization term of the variational model. In recent years, with the deeper understanding of the image prior knowledge, the technology of sparse and redundant representation is widely used in image processing. It can learn adaptively the redundant dictionary from the observed data, so the representation of the image patches in concern based on the adaptive dictionary is more effective.In the thesis, we employ the techniques of variational model and sparse and redundant representation to study the typical problems in image restoration. The main work and innovations are listed as follows:1. The restoration of images contaminated by impulse noise with high noise ratio has been studied. We focus on the random-valued impulse noise and propose a hierarchical decision-based detail-preserving variational restoration method. Firstly, the ideas of window variation and sequential detection are merged into the adaptive centre weighted median filter based noise detection technology. We not only select the possible noisy pixels with a low error rate, but also label them with different noise marks according to the differences in grey levels between a noisy pixel and its neighbours. Secondly, a detail-preserving variational model with a variable regularization parameter decided by the value of noise mark is designed. The Jacobi-type relaxation algorithm is employed to minimize the variational model. Then, the noise candidates are all updated and the true information hidden under the noisy pixels is restored. At the same time, the noise-free pixels are kept unchanged and a restored image is obtained. Benifitted from the good performance of noise detection and the advantages of-f,-norm data-fidelity combined with edge-preserving smooth regularization term for impulse noise, we can not only remove the impulse noise well, but also revert the real information about edges and details greatly, even in the situation of high noise ratio. Besides, we offer a method to estimate the noise ratio of a corrupted image roughly. So, if the noise ratio is unknown beforehand, it can be used to do estimation.2. The restoration of images contaminated by mixed noise has been studied. We focus on the problem of additive Gaussian noise plus random-valued impulse noise. In order to construct an accurate variational restoration model, we classify the noisy pixels into Gaussian or impulse type in advance based on the absolute difference image and Bayesian decision theory. Next, we extract a number of signal examples from the noisy image itself and utilize the Masked K-SVD dictionary learning method to train an adaptive redundant dictionary from the effective information contained in the examples. Then, an accurate variational model which includes an optional data-fidelity term decided by noise type and a regularization term respecting sparse representation of every image patch over the adaptive redundant dictionary is constructed. The restored image is obtained through the block-coordinate descent algorithm to minimize the variational model. Benifitted from the accuracy of noise classification and variational model, the real information about edges and textures can be reverted well in our restored image, especially for the corrupted images with rich textures. Besides, we extend the designed variational model into the restoration of image contaminated by the arbitrary combination of Gaussian and impulse noise and the problem of image inpainting. The results show that this model can cope with various situations and the restored images are satisfactory. It validates the universal application of the designed variational model in the noisy image.3. The restoration of low resolution (LR) image has been studied. We focus on the problem of single image super resolution. In the condition of the known LR image degradation model, we learn from an external training set containing various high resolution (HR) images to help promote the performance of resolution recovery. Under the restoration framework based on example learning and sparse representation, we merge the classification of image patches and the extension of edge patches into it skillfully. It makes the learned redundant dictionaries have the richer atom types and the better abilities to represent sparsely the image patches. In the premise of assurance of good dictionary quality, a fast way to learn the dictionary-pair is employed to accelerate the training process. In restoration, the input LR image is firstly split into the overlapped patches and then each patch is put into a classifier which guides to choose the dictionary-pair. Then, the sparse representation coefficient of the LR signal over the selected LR dictionary is inferred using a sparsity-adjustable OMP algorithm and the HR image patch can be reconstructed. After combining all the reconstructed patches rationally and further modification, we can get the final restored HR image. The analysis reveals that the above HR image reconstruction is actually a special case of the sparse and redundant representation based variational restoration method which is universal in some problems of image restoration.