Lapped transform domain denoising using hidden Markov trees

Algorithms based on wavelet-domain hidden Markov tree (HMT) have demonstrated excellent performance for image denoising. The HMT model is able to capture image features across the scales, in contrast to classical shrinkage that thresholds subbands independently. In this work, we extend the aforementioned results to a lapped transform domain. Lapped transforms (LT) are M-channel linear phase filter banks. Their use is motivated by their good energy compaction properties and robustness to oversmoothing. It is also observed that LT preserve better oscillatory image components, such as textures. Since LT are applied as block transforms, the transforms coefficients are rearranged into an octave-like decomposition, and their statistics are modeled by the same HMT structure as in the wavelet case. At moderate noise levels, the proposed algorithm is able to improve the results obtained with wavelets, subjectively and objectively.