Abstract
Image restoration is a fundamental problem in various areas of imaging sciences. This paper presents a class of adaptive proximal point algorithms (APPA) with contraction strategy for total variational image restoration. In each iteration, the proposed methods choose an adaptive proximal parameter matrix which is not necessary symmetric. In fact, there is an inner extrapolation in the prediction step, which is followed by a correction step for contraction. And the inner extrapolation is implemented by an adaptive scheme. By using the framework of contraction method, global convergence result and a convergence rate of O(1/N) could be established for the proposed methods. Numerical results are reported to illustrate the efficiency of the APPA methods for solving total variation image restoration problems. Comparisons with the state-of-the-art algorithms demonstrate that the proposed methods are comparable and promising.
Highlights
Image restoration is a fundamental problem in various areas of applied sciences such as medical imaging, microscopy, astronomy, film restoration, and image and video coding
This paper presents a class of adaptive proximal point algorithms (APPA) with contraction strategy for total variational image restoration
We would like to present the APPA algorithm applying to total variational (TV) image restoration as follows
Summary
Image restoration is a fundamental problem in various areas of applied sciences such as medical imaging, microscopy, astronomy, film restoration, and image and video coding. In [38], the authors developed duality-based gradient projection algorithms for total variation image restoration problems. Since the seminal work of Arrow, Hurwicz and Uzawa [1, 4], classical methods based on the gradient/subgradient for solving the saddle point problem have been proposed. In [39], Zhu and Chan proposed a primal-dual hybrid gradient (PDHG) algorithm to solved the saddle-point problem. When θ = 0 with τ, σ are made adaptive, the primal-dual procedure (4) become primal-dual hybrid gradient (PDHG) algorithm proposed in [39]. In [12], the authors show that for B being the identity, the primal-dual procedure (4) reduces to the Douglas Rachford splitting algorithm [16], and it can be regarded as a preconditioned version of the alternating direction method of multipliers.
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