Image Denoising viaL0Gradient Minimization with Effective Fidelity Term

Wenxue Zhang,Yunlei Wen,Yongzhen Cao,Lingling Li,Rongxin Zhang

doi:10.1155/2015/712801

Abstract

TheL0gradient minimization (LGM) method has been proposed for image smoothing very recently. As an improvement of the total variation (TV) model which employs theL1norm of the gradient, the LGM model yields much better results for the piecewise constant image. However, just as the TV model, the LGM model also suffers, even more seriously, from the staircasing effect and the inefficiency in preserving the texture in image. In order to overcome these drawbacks, in this paper, we propose to introduce an effective fidelity term into the LGM model. The fidelity term is an exemplar of the moving least square method using steering kernel. Under this framework, these two methods benefit from each other and can produce better results. Experimental results show that the proposed scheme is promising as compared with the state-of-the-art methods.

Highlights

Noise is inevitable in the process of image acquisition and transmission, which brings great trouble to the subsequent image analysis; image denoising is the most fundamental research topic in the community of image processing and computer vision
The state-of-the-art denoising algorithms can be categorized as (1) those taking advantage of nonlocal similarity of patches in the image: such methods include the nonlocal mean (NL-Mean) [1], BM3D [2], and PLOW [3]; in [4], the author presented a tutorial on these stateof-the-art denoising methods, and it has been shown that the LARK [5] takes the bilateral filter [6] and the nonlocal mean (NLM) [1] as special cases and they are closely related to the anisotropic diffusion [7]; (2) variational and partial differential equations- (PDEs-) based methods, such as the anisotropic diffusion [7], total variation [8], and related works [9,10,11,12,13,14]; and (3) sparse representation based method, such as the K-SVD [15] and nonlocal sparse works [16, 17]
We will demonstrate the performance of the proposed method and make a comparison with several stateof-the-art methods including NL-Mean [1], LARK [5], BLF [6], total variation (TV) [8], K-SVD [15], L0 gradient minimization (LGM) [22], and LMMSE [29]

Summary

Introduction

Noise is inevitable in the process of image acquisition and transmission, which brings great trouble to the subsequent image analysis; image denoising is the most fundamental research topic in the community of image processing and computer vision. The partial differential equations (PDEs) have been justified as effective tools for image smoothing during the last two decades, which are able to achieve a good tradeoff between noise removal and edge-preserving. The characteristic of these approaches is that it takes the form of an unconstrained regularized data fitting model, where the desired image is obtained as a regularized minimizer to a certain functional which contains both regularization and fidelity terms. One of the most popular methods in this framework is the total variation (TV) method [8, 11, 13, 14, 20, 21] It can be described as an unconstrained problem with L1 norm of the gradient as the regularization term. The specific objective function is expressed as muin ∑ (u (xi) − f (xi)) i (2)

Objectives

Results

Conclusion