Journal of Sensors

Volume 2016 (2016), Article ID 2019569, 6 pages

http://dx.doi.org/10.1155/2016/2019569

## An Edge-Preserved Image Denoising Algorithm Based on Local Adaptive Regularization

^{1}Information Engineering Department, Hubei University for Nationalities, Enshi 445000, China^{2}Digital Media College, Sichuan Normal University, Chengdu 610068, China

Received 19 March 2015; Revised 1 July 2015; Accepted 12 July 2015

Academic Editor: Marco Anisetti

Copyright © 2016 Li Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Image denoising methods are often based on the minimization of an appropriately defined energy function. Many gradient dependent energy functions, such as Potts model and total variation denoising, regard image as piecewise constant function. In these methods, some important information such as edge sharpness and location is well preserved, but some detailed image feature like texture is often compromised in the process of denoising. For this reason, an image denoising method based on local adaptive regularization is proposed in this paper, which can adaptively adjust denoising degree of noisy image by adding spatial variable fidelity term, so as to better preserve fine scale features of image. Experimental results show that the proposed denoising method can achieve state-of-the-art subjective visual effect, and the signal-noise-ratio (SNR) is also objectively improved by 0.3–0.6 dB.

#### 1. Introduction

In the process of image acquisition and transmission, all recording devices have traits which make them susceptible to noise. Noise deteriorates the quality of image and causes difficulty in image observation, feature extraction, and image analysis. In order to effectively reduce noise, some filters such as mean filter and Gaussian filter are applied on the noisy image. It is limited that filters can lose large edge and texture information of image in denoising process. In order to avoid this problem, many researchers have been working on different denoising methods. Weickert proposed a partial differential equation (PDE) method which can effectively remove noise [1]. Chan and Esedoglu proposed a total variation method based on L1 norm; it produced stair effect in smoothing area [2]. Bo and Li used a symmetric four-order PDE method to achieve acceptable denoising result [3]. Xu and Wang introduced nonlocal means into regularization to obtain a denoising version; this method oversmoothed image edges and details [4]. Gupta and Kumar proposed a generalized total variation denoising model, which can remove false edge, but it is sensitive to the selection of factor [5]. Liu and Zeng proposed a map image adaptive regularization denoising method to get a good visual effect [6]. These methods can improve the image denoising quality in some extent but destroy high-frequency information of image inevitably. In recent years, Liu and Huang proposed a new nonlocal total variation regularization algorithm for image denoising [7]. Chen et al. proposed an adaptive denoising model by regulating regularization and fidelity total variation [8]. Suman used adaptive median filter into image denoising and got good result [9]. Yan and Lu added least squares fidelity in imaging denoising by generalized total variation regularization [10]. Anilet and Hati combined curvelet transform and wiener filter to effectively reduce noise in an image [11]. Liu et al. discussed many methods in image fusion and image denoising, which all are useful and popular [12]. Abovementioned image denoising methods achieve acceptable denoising effect, but the selection of an appropriate regularized factor and reasonable iteration is still a problem. For this reason, the goal of this study is to examine efficient and reliable image denoising algorithms. This paper proposed an image denoising method based on local adaptive regularization, which can adaptively adjust denoising according to different area of noisy image and better protect the texture and details of image, so as to achieve state-of-the-art denoising effect.

The rest of this paper is organized as follows. The introduction of regularization (especially for total variation regularization) is described in Section 2. Further, Section 3 details main idea of the proposed method in this paper. And experimental results are presented in Section 4. Finally, summary and outlook are discussed in Section 5, that is, the conclusion of this paper.

#### 2. Total Variation Denoising

In signal processing, total variation denoising is remarkably effective at simultaneously preserving edges whilst smoothing away noise in flat regions, even at low signal-to-noise ratios. It is based on the principle that signals with excessive and possibly spurious detail have high total variation (TV); that is, the integral of the absolute gradient of the signal is high. According to this principle, reducing the total variation of the signal subject to its being a close match to the original signal removes unwanted detail whilst preserving important details such as edges. The concept of total variation was pioneered by Rudin et al. [13]. In area of image processing, suppose is the original image, is the noisy version of , and this relation can be mathematically expressed by

Here is random noise with zero mean and variation. At the same time, we can, for example, define the total variation as ; the goal of TV denoising is to find an approximation, which is smaller but close to the one before. That is, TV denoising is a minimization process; it explores the equal state of energy function relative to the TV norm of and the regularization of , expressed in

Here represents the domain of image, all pixels . Normally the TV of ideal image is smaller than noisy image, so minimizing TV can reduce the noise of image. Based on this principle, (2) can be equaled as follows:

The first term in (3) is data fidelity term, which can retain characteristics of the original image and reduce distortion. The second term in (3) is regularization term, which depends on noise level and balance denoising and smoothing. The Euler-Lagrange equation derivate from (3) is represented by

Here is a diffusion coefficient. In edge of image, large will lead to small diffusion coefficient, so the diffusion along edge is weak to preserve edge of image. In smoothing area of image, small will lead to large diffusion coefficient, so the diffusion in smoothing area is strong to remove noise in image. The regularization parameter plays a critical role in the denoising process. When , there is no denoising and the result is identical to the input signal. As , however, the total variation term plays an increasingly strong role, which forces the result to have smaller total variation, at the expense of being less like the input (noisy) signal. Thus, the choice of regularization parameter is critical to achieving just the right amount of noise removal.

#### 3. Image Denoising Method Based on Local Adaptive Regularization

Referring to the classical TV model which described in Section 2, it can reduce noise by energy constraint, however, the selection of an appropriate regularization factor is also a difficult problem. High brings oversmoothing and small reduces noise ineffectively. In order to handle impulsive noisy image, an appropriate regularization factor must be obtained to reduce different noise in image, which aims at balance of data fidelity term and regularization term. For these discussions, a novel image denoising method based on local adaptive regularization is proposed here. According to noise level in different image area, it defines a space variable energy function and can adaptively adjust denoising degree. In order to clearly elaborate idea, the main steps described are as follows.

*Step 1 (global residual noisy energy computation). *This step produces the residual error of noise in input image. Suppose input noisy image is . Estimated denoising version of is obtained by classical TV regularization, which is expressed as . Then, global residual noisy energy can be computed by expression . Therefore, the mean value of global residual error is computed and named as .

*Step 2 (local energy computation). *On the basis of first step, local variance of residual image can be expressed by , where is a normalized and radial symmetric smoothing-window and . Suppose to get prior information of noise energy in noisy image; here is noise standard deviation of input noisy image .

*Step 3 (iteratively compute regularization factor to achieve local adaptive regularization). *Define and suppose . Compute ; regularization factor is then computed by . In this way, each iteration of can be applied to (4) to obtain an estimated denoising version. When condition of convergence is satisfied, the final denoising result can be achieved.

#### 4. Experiments and Discussion

In this section, we validate the potential of the proposed method by simulated noisy image experiment and real noisy image experiment. The comparison we provide here is the denoising results by classical TV denoising, bilateral filtering, and the denoising method proposed in [4].

##### 4.1. Simulated Noisy Image

###### 4.1.1. Salt and Pepper Noise

Firstly, the test image woman was additive with salt and pepper noise, at which variance is 0.02. In order to better show different denoising comparison, experimental result shown here is the enlarged local area of woman.

Figure 1(a) is the clear original woman image, Figure 1(b) is seen to contain a large number of salt and pepper noises and many noise points contaminate image, Figure 1(c) is the denoising result of classical TV method, here texture in the right smoothing part of image is preserved, and conversely woman’s face detailed information is lost and edge of image is not ideal, Figure 1(d) is the denoising result by bilateral filter, which is more fuzzy and noisy, and the visual effect is bad, and Figure 1(e) is the denoising result by method in [4] and noise is removed in this result; however the overall effect is oversmoothing. The denoising result in Figure 1(f) is clear and details are preserved well, although there are still a few grain noises, but it does not affect the general viewing effect.