Independent component analysis (ICA) is a statistical technique which attempts to nd a representation of observed data such that the components are as independent as possible. This technique has shown great promise in feature extraction, essentially nding the building blocks of any given data. In particular, when applied to image data ICA gives a representation which identies the contours in the image; these can be considered the primary structure in the data. The term noise refers to any random degradation of a signal. This thesis is concerned with noise in two-dimensional signals, i.e. images. Such noise may be due to disturbances inherent in image acquisition or could result from a noisy transmission channel over which the image is sent. Either way, the denoising task is to use the information we have on the statistical structure of images to remove the eoeect of the noise as well as possible. This work applies ICA and related techniques to denoising images. First, a general framework for denoising random vectors is introduced; then it is applied to the specic case of image data. Finally, extensive tests are performed, comparing the proposed method to traditional denoising methods.
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