Solving total-variation image super-resolution problems via proximal symmetric alternating direction methods

Ying Tong,Fenggang Sun,Bin Gao,Shiming Xu

doi:10.1186/s13660-016-1136-7

Abstract

The single image super-resolution (SISR) problem represents a class of efficient models appealing in many computer vision applications. In this paper, we focus on designing a proximal symmetric alternating direction method of multipliers (SADMM) for the SISR problem. By taking full exploitation of the special structure, the method enjoys the advantage of being easily implementable by linearizing the quadratic term of subproblems in the SISR problem. With this linearization, the resulting subproblems easily achieve closed-form solutions. A global convergence result is established for the proposed method. Preliminary numerical results demonstrate that the proposed method is efficient and the computing time is saved by nearly 40% compared with several state-of-the-art methods.

Highlights

single image super-resolution (SISR) is a technique that aims at restoring a high-resolution (HR) image from a single degraded low-resolution (LR) image
To alleviate the above dilemma and further apply FSR-ADMM into wider scenarios with proper matrix A, we propose a new method with two-fold solution. ( ) Compute
In light of the above analysis, this paper proposes the following iterative scheme based on semiproximal symmetric ADMM (FSR-symmetric alternating direction method of multipliers (SADMM)):b xk+ =

Summary

Introduction

SISR is a technique that aims at restoring a high-resolution (HR) image from a single degraded low-resolution (LR) image. Zhao et al [ ] proposed a fast single image super-resolution by adopting a new efficient analytical solution for -norm regularized problems, which can reduce the number of iterations in each loop from five steps to three steps by tackling the downsampling operator and the blurring operator H simultaneously. A) is the classical least square problem and has the solution given by xk+ = HT T H + μATA – HT Ty + μAT uk – dk As to such an expensive inversion process, the methods to alleviate the computational burden can be roughly categorized into two main categories, one is to ideally assume ATA = I. In light of the above analysis, this paper proposes the following iterative scheme based on semiproximal symmetric ADMM (FSR-SADMM):b xk+ =. We denote by ∗ the solution set of VI( , F, θ )

Some notations

Nh and

Conclusions