Image Restoration Using a Fixed-Point Method for a TVL2 Regularization Problem

Kyoum Sun Kim,Jae Heon Yun

doi:10.3390/a13010001

Abstract

In this paper, we first propose a new TVL2 regularization model for image restoration, and then we propose two iterative methods, which are fixed-point and fixed-point-like methods, using CGLS (Conjugate Gradient Least Squares method) for solving the new proposed TVL2 problem. We also provide convergence analysis for the fixed-point method. Lastly, numerical experiments for several test problems are provided to evaluate the effectiveness of the proposed two iterative methods. Numerical results show that the new proposed TVL2 model is preferred over an existing TVL2 model and the proposed fixed-point-like method is well suited for the new TVL2 model.

Highlights

Image restoration is the fundamental problem in image processing that recovers a true image from a blurry and noisy image
We provide numerical results for four test images that are listed in Tables 1–4 and values for the blurred and noisy image f, “peak signal-to-noise ratio (PSNR)” represents the PSNR values for the restored image, “Iter” denotes the number of iterations required for Algorithms 1–5, the values in parentheses under the “Iter” column refer to the average number of iterations for CGLS, and “α, β, γ, λ” and “δ” denote parameters that are chosen by numerical tries
This means that the fixed-point-like method for TVL2 problem (4) restores the true image better than the fixed-point methods for TVL2 problems (3) and (4)

Summary

Introduction

Image restoration is the fundamental problem in image processing that recovers a true image from a blurry and noisy image. The problem of image restoration usually reduces to find the optimal solution u ∈ Rm based on the following model: f = Au + ε, (1). Our purpose is to restore the original image u from blurred and noisy image f as well as possible. Over the past few decades, optimization techniques and various variation models [1,2,3]. The well-known ROF (Rudin–Osher–Fatemi) total variation model [3] produces the deblurred image given by the following minimization problem: min k Au − f k22 + βTV (u) , (2).

Objectives

Results

Conclusion