4 Wavelet Denoising for Image Enhancement

Image processing is a science that uncovers information about images. Enhancement of an image is necessary to improve appearance or to highlight some aspect of the information contained in the image. Whenever an image is converted from one form to another, e.g., acquired, copied, scanned, digitized, transmitted, displayed, printed, or compressed, many types of noise or noiselike degradations can be present in the image. For instance, when an analog image is digitized, the resulting digital image contains quantization noise; when an image is halftoned for printing, the resulting binary image contains halftoning noise; when an image is transmitted through a communication channel, the received image contains channel noise; when an image is compressed, the decompressed image contains compression errors. Hence, an important subject is the development of image enhancement algorithms that remove (smooth) noise artifacts while retaining image structure. Digital images can be conveniently represented and manipulated as matrices containing the light intensity or color information at each spatially sampled points. The term monochrome digital image or simply digital image, refers to a two-dimensional light intensity function f(n1, n2), where n1 and n2 denote spatial coordinates, the value of f(n1, n2) is proportional to the brightness (or gray level) of the image at that point, and n1, n2, and f(n1, n2) are integers. The problem of image denoising is to recover an image f(n1, n2) from the observation g(n1, n2), which is distorted by noise (or noise-like degradation) q(n1, n2); i.e.,