Hidden Markov tree image denoising with redundant lapped transforms

Hidden Markov tree (HMT) wavelet models have demonstrated superior performance in image filtering, by their ability to capture features across scales. Recently, we proposed to extend the HMT framework to the lapped transform domain, where lapped transforms (LT) are M-channel linear phase filterbanks. When the number of channels is a power of 2, the block partition provided by LT is remapped to an octave-like representation, where an HMT is able to model the statistical dependencies between intra- and interband coefficients. Due to better energy compaction and reduced aliasing properties, LT outperforms discrete wavelet transforms at moderate noise levels, both subjectively and objectively. However, critically-decimated LT suffers from a lack of shift-invariance, resulting in a degraded performance. We study the improvement of HMT modeling in the LT domain (HMT-LT), combined with a redundant decomposition, in order to increase its performance for image denoising.