Morphological wavelet transform with adaptive dyadic structures

We propose a two component method for denoising multidimensional signals, e.g. images. The first component uses a dynamic programing algorithm of complexity O (N log N) to find an optimal dyadic tree representation of a given multidimensional signal of N samples. The second component takes a signal with given dyadic tree representation and formulates the denoising problem for this signal as a Second Order Cone Program of size O (N). To solve the overall denoising problem, we apply these two algorithms iteratively to search for a jointly optimal denoised signal and dyadic tree representation. Experiments on images confirm that the approach yields denoised signals with improved PSNR and edge preservation.