Image restoration via the adaptive \(TV^p\) regularization. (English) Zbl 1446.94012
Summary: To keep structures in the restoration problem is very important via coupling the local information of the image with the proposed model. In this paper we propose a local self-adaptive \(\ell^p\)-regularization model for \(p\in(0,2)\) based on the total variation scheme, where the choice of \(p\) depends on the local structures described by the eigenvalues of the structure tensor. Since the proposed model as the classic \(\ell^p\) problem unifies two classes of optimization problems such as the nonconvex and nonsmooth problem when \(p\in(0,1)\), and the convex and smooth problem when \(p\in(1,2)\), it is generally challenging to find a ready algorithmic framework to solve it. Here we propose a new and robust numerical method via coupling with the half-quadratic scheme and the alternating direction method of multipliers (ADMM). The convergence of the proposed algorithm is established and the numerical experiments illustrate the possible advantages of the proposed model and numerical methods over some existing variational-based models and methods.
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 65K05 | Numerical mathematical programming methods |
| 65R32 | Numerical methods for inverse problems for integral equations |
Keywords:
image restoration; proximal point scheme; half quadratic scheme; alternating direction method of multipliers (ADMM); structure tensorReferences:
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