ABSTRACT

Denoising is one of the fundamental problems in digital image processing and can be defined as the removal of noise from observed image data, for example in broadcast and surveillance as well as in medical imaging applications. Often performed as a preprocessing step prior to any analysis or modeling of the images, denoising improves the image quality thus reducing the effects of noise on the output of any subsequent operations. Let f(r) denote some original image data corrupted by additive white Gaussian noise n(r), resulting in observed image data g(r), where r denotes the n-dimensional coordinates of the image data, and n 2 f2, 3, 4g. For n ¼ 2, r usually represents the horizontal and vertical coordinates (often denoted by x and y), whereas for n ¼ 4 for instance in case of real-time capture of three-dimensional (3-D) images (such as fMRI image data), r may be composed of the three spatial coordinates (x, y, and z) and a time coordinate. Corruption of the original image data can, therefore, be expressed in the following form,

g(r) ¼ f (r)þ n(r) (27:1)

where n ¼ N (0, s2) denotes uncorrelated, zero-mean, Gaussian noise with a standard deviation of s. The addition of white Gaussian noise often takes place at the imaging side, for instance due to the finite exposure time of the imaging devices, thermal noise in the CCD arrays, quantization noise, or a combination of some or all of these. The problem of image denoising can be stated as follows.