IEEE Trans Image Process - An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems.

Tópicos

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Resumo

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art.

Resumo Limpo

propos new fast algorithm solv one standard approach illpos linear invers problem iplip possibl nonsmooth regular minim constraint solut explain observ suffici well although regular constraint usual convex sever particular featur problem huge dimension nonsmooth preclud use offtheshelf optim tool stimul consider amount research paper propos new effici algorithm handl one class constrain problem often known basi pursuit denois tailor imag recoveri applic propos algorithm belong famili augment lagrangian method can use deal varieti imag iplip includ deconvolut reconstruct compress observ mri use either totalvari waveletbas general framebas regular propos algorithm instanc socal altern direct method multipli converg suffici condit known show condit satisfi propos algorithm experi set imag restor reconstruct benchmark problem show propos algorithm strong contend stateoftheart

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