Research On Bregman Iterative Regularization Methods For Image Restoration

With the development of modern communication technologies, as important sources of information acquisition and media of information exchange, images and videos are gaining increasingly broader applications both in social life and at work. Due to the impact of a variety of physical equipment, physical conditions and human factors, the images obtained will inevitably decline in quality, probably to the extend that does not meet the application requirements. As a result, there is a demand to process the degraded images and restore the high-definition, high-quality images close to the originals. This is the main goal of image restoration.As a low-level vision technology, image restoration not only reproduce high-quality images, but also laid a good foundation for middle-and high-level vision technologies. It has been widely studied, and has important applications in astronomy, remote sensing, medical engineering, industrial engineering, culture, arts, military, public security fields, and so on.This article is mainly based on Bregman iterative regularization techniques. In this paper, the image restoration problem is discussed in-depth from the perspective of the regular model and iterative algorithm level.This study has the following main aspects:First, on the subjects of image restoration research background, the current research status and the existing key techniques in image restoration, this paper provides a simple analysis and a summary. We analyzed a variety of image degradation model, provided a brief introduction to the image restoration method based on the traditional regularization and the associated rapid iteration image restoration algorithm, and proposed the objective criteria and subjective criteria for image quality evaluation.Then, based on the traditional regularization image restoration methods, this paper introduced an iterative regularization technique, and proposed an image restoration method based on Bregman iterative dual regularization.This method combines total variation and wavelet dual regularization techniques, unifies them under Bregman iterative regularization framework, and uses split Bregman algorithm to perform fast image restoration.Experimental results show that for the general Gaussian noise pollution blurred images, the proposed algorithm not only can recover quickly, but better than some representative image restoration algorithms, such as the Gaussian model-based Bayesian method, GPSR method, the non-local total variational method.General image restoration techniques mainly address blurred images caused by Gaussian noise pollution. It remains difficult to effectively handle fuzzy images caused by other types of noise pollution. In view of this deficiency, this paper studied the image restoration problem for blurred images caused by impulse noise pollution, and proposed a two-step image restoration algorithm. We first gave a quick simple algorithm to eliminate impulsive noise, and then established an image deblurring framework based on L1 norm fidelity item, and using split Bregman iterative algorithms for fast solution.The results show that for heavy impulse noise pollution blurred image, the proposed restoration algorithm is still able to recover effectively.Finally, this study applied the proposed gray-scale image restoration methods on the multi-channel image restoration problems, mainly targeting the color image restoration problem. We first set up the total variation model for the color images, and then established different image restoration models for Gaussian noise pollution blurred images and impulse noise pollution blurred images, respectively, and using split Bregman iterative algorithm for root finding. Experimental results show that for different orders of magnitude of the two types of noise and different types of fuzzy images, the proposed algorithm can perform efficient image restoration.