The Restoration of Textured Images Using Fractional-Order Regularization

Ying Fu,Jiliu Zhou,Lei Liang,Xiaohua Li,Yi Zhang

doi:10.1155/2014/356906

Abstract

Image restoration problem is ill-posed, so most image restoration algorithms exploit sparse prior in gradient domain to regularize it to yield high-quality results, reconstructing an image with piecewise smooth characteristics. While sparse gradient prior has good performance in noise removal and edge preservation, it also tends to remove midfrequency component such as texture. In this paper, we introduce the sparse prior in fractional-order gradient domain as texture-preserving strategy to restore textured images degraded by blur and/or noise. And we solve the unknown variables in the proposed model using method based on half-quadratic splitting by minimizing the nonconvex energy functional. Numerical experiments show our algorithm's robust outperformance.

Highlights

The image degradation is modeled as y = x ⊗ h + n, (1)where x is the original latent image and y is an observed image degraded by blur and/or noise, which is produced by convolving x with a blur point-spread-function (a.k.a. kernel) h and adding zero mean Gaussian noise n
We introduce the sparse prior in fractional-order gradient domain as texture-preserving strategy to restore textured images degraded by blur and/or noise
This paper presents fractional-order regularization for the restoration of textured image degraded by blur and/or additive noise

Summary

Introduction

Where x is the original latent image and y is an observed image degraded by blur and/or noise, which is produced by convolving x with a blur point-spread-function (a.k.a. kernel) h and adding zero mean Gaussian noise n. Image restoration is ill-posed problem, so many methods introducing priors based on natural image statistics can regularize it. The gray values between neighboring pixels have high correlation This highly self-similar fractal information of image fractal information is usually represented by complex textural features, and the works in [12,13,14,15,16,17,18] showed that fractional-order gradient is more suitable to deal with fractal-like textures. Different from work in [18], the sparse prior in fractional-order gradient domain is considered in our work, which is more suitable for the texture of image. This paper presents fractional-order regularization for the restoration of textured image degraded by blur and/or additive noise.

Motivation

The Proposed Model and Algorithm

Numerical Experiments

Conclusion