Solving constrained total-variation image restoration and reconstruction problems via alternating direction methods. (English) Zbl 1217.65071

Ng, Michael K.; Weiss, Pierre; Yuan, Xiaoming

SIAM J. Sci. Comput. 32, No. 5, 2710-2736 (2010).

Summary: We study alternating direction methods for solving constrained total-variation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting, and image cartoon + texture decomposition. As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.

MSC:

65F22	Ill-posedness and regularization problems in numerical linear algebra
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry
94A08	Image processing (compression, reconstruction, etc.) in information and communication theory

Keywords:

total-variation; image restoration; image reconstruction; alternating direction method; augmented Lagrangian; numerical examples; regularization

Software:

RecPF