Total Variation Image Restoration Method Based on Subspace Optimization

Xiaoguang Liu,Xingbao Gao

doi:10.1155/2018/6921742

Abstract

The alternating direction method is widely applied in total variation image restoration. However, the search directions of the method are not accurate enough. In this paper, one method based on the subspace optimization is proposed to improve its optimization performance. This method corrects the search directions of primal alternating direction method by using the energy function and a linear combination of the previous search directions. In addition, the convergence of the primal alternating direction method is proven under some weaker conditions. Thus the convergence of the corrected method could be easily obtained since it has same convergence with the primal alternating direction method. Numerical examples are given to show the performance of proposed method finally.

Highlights

Digital image restoration has a wide application in various areas including Navigation, Aerospace, and Biomedicine
Where b ∈ Rq is the additive noise and the spatial-invariant matrix A ∈ Rq×p represents the degradation system caused by problems such as motion blur, distortion radiation, and distortion wavelets in seismic imaging, p = p1p2 with p1 and p2 being the number of rows and columns, respectively, when images are expressed as a matrix
The objective of the image restoration is to estimate the original image faccording to some a priori knowledge about the degradation system A, the additive noise b, and the observed image g

Summary

Introduction

Digital image restoration has a wide application in various areas including Navigation, Aerospace, and Biomedicine (see [1,2,3] and the references therein). Where b ∈ Rq is the additive noise and the spatial-invariant matrix A ∈ Rq×p represents the degradation system caused by problems such as motion blur, distortion radiation, and distortion wavelets in seismic imaging, p = p1p2 with p1 and p2 being the number of rows and columns, respectively, when images are expressed as a matrix. The objective of the image restoration is to estimate the original image faccording to some a priori knowledge about the degradation system A, the additive noise b, and the observed image g. One of the effective ways to solve these problems is to combine some a priori information of the original image and define the regularization solution; that is, f∗ is a minimizer of the following cost (energy) function:

Methods

Results

Conclusion