Efficient Iterative Regularization Method for Total Variation-Based Image Restoration

Ge Ma,Ziwei Yan,Zhijia Zhao,Zhifu Li

doi:10.3390/electronics11020258

Abstract

Total variation (TV) regularization has received much attention in image restoration applications because of its advantages in denoising and preserving details. A common approach to address TV-based image restoration is to design a specific algorithm for solving typical cost function, which consists of conventional ℓ2 fidelity term and TV regularization. In this work, a novel objective function and an efficient algorithm are proposed. Firstly, a pseudoinverse transform-based fidelity term is imposed on TV regularization, and a closely-related optimization problem is established. Then, the split Bregman framework is used to decouple the complex inverse problem into subproblems to reduce computational complexity. Finally, numerical experiments show that the proposed method can obtain satisfactory restoration results with fewer iterations. Combined with the restoration effect and efficiency, this method is superior to the competitive algorithm. Significantly, the proposed method has the advantage of a simple solving structure, which can be easily extended to other image processing applications.

Highlights

Due to the imperfections of an imaging system, images often tend to be corrupted by noise and blur during image capture, transmission, and storage, resulting in image degradation
Due to its superior ability in denoising and detail-preserving, we focus on Total variation (TV) regularization that is widely used in various image restoration tasks
By constructing a pseudoinverse matrix, an equivalent seminorm fidelity term is imposed on TV-based image restoration problem (3)

Summary

Introduction

Due to the imperfections of an imaging system, images often tend to be corrupted by noise and blur during image capture, transmission, and storage, resulting in image degradation. The essence of these methods is still gradient descent, whose main drawbacks are their speed of convergence and sensitivity of noise Another series of algorithms for solving (2) is based on the splitting method, decoupling the difficult TV regularization problem (2) into separate subproblems, which can be solved efficiently by iterative minimization. Due to the expansibility and effectiveness of split methods, ADMM and split Bregman were widely used in the fields of image restoration, denoising, and deblurring. Motivated by the above studies, we aim to design a novel TV-based optimization model and algorithm to improve the effect and efficiency of image restoration. By constructing a pseudoinverse matrix, an equivalent seminorm fidelity term is imposed on TV-based image restoration problem (3) This improvement can eliminate the negative effect caused by the null space of H;.

Related Work

The Proposed Algorithm

Conclusions