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 sub-band 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.