Kazerouni, AbbasKamilov, Ulugbek S.Bostan, EmrahUnser, Michael2013-03-282013-03-282013-03-28201310.1109/Lsp.2013.2242061https://infoscience.epfl.ch/handle/20.500.14299/90713WOS:000314828600001We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the link between the discrete gradient and Haar-wavelet shrinkage with cycle spinning. The redundancy of the representation implies that some wavelet-domain estimates are inconsistent with the underlying signal model. However, by imposing additional constraints, our method finds wavelet-domain solutions that are mutually consistent. We confirm the MMSE performance of our method through statistical estimation of Levy processes that have sparse derivatives.Augmented LagrangianMMSE estimationtotal variation denoisingwavelet denoisingtext::journal::journal article::research article