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

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 |