Image and Video Restoration with Nonlocal Transform-Domain Filtering

Vision is the most important source of information for humans and the acquisition of images has numerous applications in science, engineering, medicine and also in consumer devices such as cameras, mobile phones, etc. Digital image acquisition, in particular, has become the most common means of producing images; it has almost fully replaced image acquisition on ...lm. A typical digital acquisition device contains lens and a solid-state image sensor. The scene radiance is focused by the lens to the sensor, which integrates the irradiance at its surface during the exposure time and produces a 2-D array of digital values (i.e. a raw image). The lens and the sensor introduce a variety of degradations such as geometrical distortions, blur, and noise. In addition to inherent technological factors that cause these degradations, there are external factors such as scene illumination and a motion within the scene or between the scene and the lens. In order to obtain images that can be visualized, raw images typically undergo some image processing such as denoising, color-...lter array interpolation (demosaicking), enhancement (sharpening), color correction, and white balancing. This thesis deals with the problems of denoising, deblurring, and enhancement of images and video. We propose a particular ...ltering algorithm, called BM3D, as the basic tool for approaching these problems. Among the multitude of existing ...ltering algorithms, BM3D is the ...rst to exploit simultaneously: 2 sparse transform-domain representations (i.e. a transform spectrum characterized by few high-magnitude coe¢cients) 2 nonlocal image modeling (manifested by self-similarity between image subsets). We show that the BM3D ...lter not only outperforms works that are based on either one of the above two approaches but is currently one of the best image-denoising methods. The main goals of this thesis are to present and study the BM3D ...lter and to show that denoising is a fundamental tool in image processing, which can be applied to various image processing problems. We accomplish these goals by ...rst studying the BM3D ...lter and some of its extensions and then presenting its application to: