Image denoising using over-complete wavelet representations

Wavelet transforms have been utilised effectively for image denoising, providing a means to exploit the relationships between coefficients at multiple scales. In this paper, a modified structure is presented that enables the utilisation of an unlimited number of wavelet filters. An alternative denoising technique is thus proposed with a simple approach for the utilisation of multiple wavelet filters. According to the probability distribution function associated with each subband of the transformed data (modelled by generalised Gaussian distribution), different denoising methods are adaptively applied. The proposed expansion is based on the use of either a Walsh-Hadamard Transform (WHT) or independent component analysis (ICA) to remove dependencies between the data streams associated with each wavelet decomposition. The application of a number of different separable wavelet combinations along the rows and columns of the image are also explored.