ABSTRACT
Many image-related inverse problems deal with the restoration of an unknown image from its degraded observation. Depending on the model of the degradation process, we could have a variety of restoration problems, such as denoising, deblurring, demosaicking, deblocking/deringing, inverse halftoning, and so on. It has been widely recognized that the a priori knowledge, in the form of either regularization functional in a deterministic setting or prior probability distribution in a statistical setting, plays a critical role in the accuracy of image processing algorithms. The task of representing the a priori knowledge for the class of photographic images is particularly challenging due to the diversity of various structures (e.g., edges, corners, lines, and textures) in natural scenes. Extensive effort has been devoted to the pursuit of good mathematical models for photographic images in recent decades.
