IEEE Trans Image Process - A generalized accelerated proximal gradient approach for total-variation-based image restoration.

Tópicos

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Resumo

This paper proposes a generalized accelerated proximal gradient (GAPG) approach for solving total variation (TV)-based image restoration problems. The GAPG algorithm generalizes the original APG algorithm by replacing the Lipschitz constant with an appropriate positive-definite matrix, resulting in faster convergence. For TV-based image restoration problems, we further introduce two auxiliary variables that approximate the partial derivatives. Constraints on the variables can easily be imposed without modifying the algorithm much, and the TV regularization can be either isotropic or anisotropic. As compared with the recently developed APG-based methods for TV-based image restoration, i.e., monotone version of the two-step iterative shrinkage/thresholding algorithm (MTwIST) and monotone version of the fast IST algorithm (MFISTA), our GAPG is much simpler as it does not require to solve an image denoising subproblem. Moreover, the convergence rate of O(k(-2)) is maintained by our GAPG, where k is the number of iterations; the cost of each iteration in GAPG is also lower. As a result, in our experiments, our GAPG approach can be much faster than MTwIST and MFISTA. The experiments also verify that our GAPG converges faster than the original APG and MTwIST when they solve identical problems.

Resumo Limpo

paper propos general acceler proxim gradient gapg approach solv total variat tvbase imag restor problem gapg algorithm general origin apg algorithm replac lipschitz constant appropri positivedefinit matrix result faster converg tvbase imag restor problem introduc two auxiliari variabl approxim partial deriv constraint variabl can easili impos without modifi algorithm much tv regular can either isotrop anisotrop compar recent develop apgbas method tvbase imag restor ie monoton version twostep iter shrinkagethreshold algorithm mtwist monoton version fast ist algorithm mfista gapg much simpler requir solv imag denois subproblem moreov converg rate ok maintain gapg k number iter cost iter gapg also lower result experi gapg approach can much faster mtwist mfista experi also verifi gapg converg faster origin apg mtwist solv ident problem

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