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The Essential Guide to Image Processing- P9:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | 242 CHAPTER 11 Multiscale Denoising of Photographic Images coefficient by an optimized scalar value. Although these methods are quite simple they capture many of the concepts that are used in state-of-the-art denoising systems. Toward the end of the chapter we briefly describe several alternative approaches. 11.2 DISTINGUISHING IMAGES FROM NOISE IN MULTISCALE REPRESENTATIONS Consider the images in the top row of Fig. 11.3. Your visual system is able to recognize effortlessly that the image in the left column is a photograph while the image in the middle column is filled with noise. How does it do this We might hypothesize that it simply recognizes the difference in the distributions of pixel values in the two images. But the distribution of pixel values of photographic images is highly inconsistent from image to image and more importantly one can easily generate a noise image whose pixel distribution is matched to any given image by simply spatially scrambling the pixels . So it seems that visual discrimination of photographs and noise cannot be accomplished based on the statistics of individual pixels. Nevertheless the joint statistics of pixels reveal striking differences and these may be exploited to distinguish photographs from noise and also to restore an image that has been corrupted by noise a process commonly referred to as denoising. Perhaps the most obvious and historically the oldest observation is that spatially proximal pixels of photographs are correlated whereas the noise pixels are not. Thus a simple strategy for denoising an image is to separate it into smooth and nonsmooth parts or equivalently low-frequency and high-frequency components. This decomposition can then be applied recursively to the lowpass component to generate a multiscale representation as illustrated in Fig. 11.1. The lower frequency subbands are smoother and thus can be subsampled to allow a more efficient representation generally known as a multiscale pyramid 1 2 . The resulting
