Research Of Image Restoration Algorithm Based On Sparse Representation

Images may be degraded during data acquisition, transmission, and processing, because of the imaging conditions and the interference of the external environment. However, in our life, we need the high-resolution images. Thus, an important problem in image processing is the reconstruction of the original true image from a degraded image, which is the main purpose of image restoration. On the other hand, To guarantee a good performance for the subsequent image processing, such as edge detection, image segmentation, and object recognition, it is important to effectively reconstruct the original image from a degraded image while keeping its features intact. Therefore image restoration has become a fundamental problem in image processing. Image restoration is a image processing technique that recovering and reconstructing the original images from degraded images by using a priopri information of the images to establish an appropriate model. It includes an image de-noising, image deblurring, image restoration and improved several aspects of the problem resolution. This thesis main consider two problems:image denoising and image deblurring.First, the thesis introduces the background and significance of image restoration, image degraded model, and the methods of image restoration.Second, This paper presents a new approach to image deblurring, on the basis of total variation (TV) and wavelet frame. The Rudin-Osher-Fatemi model, which is based on TV minimization, has been proven to be effective for image restoration. The explicit exploitation of sparse approximations of natural images has led to the success of wavelet frame approach in solving image restoration problems. However, TV introduces staircase effects. Thus, we propose a new objective functional that combines the tight wavelet frame and TV to reconstruct images from blurry and noisy observations while mitigating staircase effects. The minimization of the new objective functional presents a computational challenge. We propose a fast minimization algorithm by employing the augmented Lagrangian technique. The experiments on a set of image deblurring benchmark problems show that the proposed method outperforms previous state-of-the-art methods for image restoration.Third, researches mainly consider the image deblurring under the Gaussian noise, however, the image also may be corrupted by impulse noise during the image acquisition, it is important to reconstruct the image from the blur and impulse noise. However, the method of image restoration for the image blur and Gaussian noise cannot be used for image deblurring with impulse noise. In this thesis, we propose a new objective functional that combines the tight framelet and TV to restore images corrupted by blur and impulsive noise while mitigating staircase effects. The minimization of the new objective functional presents a computational challenge. We propose a fast minimization algorithm by employing the augmented Lagrangian technique. The experiments on a set of image deblurring benchmark problems show that the proposed method outperforms previous state-of-the-art methods for image restoration.Finally, we propose a two-phase approach to restore images corrupted by impulsive noise based on sparse representation. In the first phase, we identify the outlier candidates--the pixels that are likely to be corrupted by impulsive noise. Then in the second phase, the image is denoised via dictionary learning by using the outlier-free data. The dictionary learning task is formulated as a modified l1-l1minimization objective and solved under the alternating direction method. The experimental results demonstrate that our method can obtain better performances in terms of both quantitative evaluation and visual quality than the state-of-the-art impulse denoising methods.