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Fixed-point algorithms for a TVL1 image restoration model. (English) Zbl 1487.94027

Summary: In this paper, we study fixed point proximity algorithms for a TVL1 restoration model recovering blurred images with impulsive noise, and image inpainting. The model that minimizes the sum of a data fidelity term in the \(\ell^1\)-norm, a term in \(\ell^2\)-norm and total-variation regularization term is strictly convex. We obtain the solution of the model through finding a fixed point of a nonlinear mapping expressed in terms of the proximity operator of the \(\ell^1\)-norm or the \(\ell^2\)-norm, each of which is explicitly given. The non-expansivity of the mapping is also analysed theoretically. This formulation naturally leads to fixed-point algorithms for numerical treatment of the model. Numerical experiments demonstrate that the proposed algorithms perform favourably.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
35A15 Variational methods applied to PDEs
49J40 Variational inequalities

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References:

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