Elsevier

Neurocomputing

Volume 71, Issues 13–15, August 2008, Pages 2986-3000
Neurocomputing

A mixed noise image filtering method using weighted-linking PCNNs

https://doi.org/10.1016/j.neucom.2007.04.015Get rights and content

Abstract

Image is often degraded by more than one type of noise. In order to design an efficient filter to remove mixed noise from image, this paper proposes a weighted-linking pulse coupled neural network (PCNN) model so as to construct a two-channel parallel noise filter using four PCNNs of this model. This filter detects noise using the pulses generated by neurons, and iteratively removes noise by the pixel signal variation of pulse neurons. The filtering parameters and the iteration stopping conditions are discussed. Experiments show that the proposed PCNN-based filtering method is fast and effective for removing single impulse noise, additional Gaussian noise, as well as the mixed noise of them.

Introduction

Causing noise is often inevitable at image acquisition, transmission and processing stages. Little noise may often severely damage image quality. Usually, noise may make image understanding and recognizing more difficult. As a result, some serious error may be caused, even a spurious conclusion may be drawn. Thus, noise should be filtered as completely as possible from image. Generally, noise filtering technology consists of two main steps: noise detection and noise removal. Furthermore, during noise filtering, these original image features, such as edges, size and shape, should be kept unchanged.

Generally, two main models are used for characterizing most noise in digital images. They are additive Gaussian noise model and impulse noise model [6]. From the viewpoint of probability, the distribution function of Gaussian noise conforms tog(x)=1σ2πe-(x-μ)2/2σ2,where -x-, σ is the standard deviation, and μ is the mean value of noise signal. If the mean value μ=0, noise signal follows exactly the additive Gaussian noise model [6], which can be formulated asIi,jn=Ii,jo+ni,j,where Ii,jn indicates the intensity of noise pixel (i,j), Ii,jo indicates the original pixel intensity and ni,j is the added noise intensity. Such a type of noise is usually generated during image acquisition. Some classical filters, such as Gaussian filter, recursive two-dimensional (2D) filter [29], adaptive Wiener filter [33], neighbors mean filter, can efficiently remove it, except that they may degrade the sharpness of object edges. To overcome this weakness, some nonlinear methods are developed [31], [35], [21], [15], [32], [17]. These methods can effectively remove Gaussian noise, however they may bring a new weakness, namely some thin lines and small objects of original image cannot be well preserved.

The other one is impulse noise model. This type of noise may be characterized by replacing the portion of pixel intensity with a random value, while keeping the remainder unchanged [6]. Generally, this impulse noise model can be formulated asIi,jn=ni,jwithprobabilityp,Ii,jowithprobability(1-p).where Ii,jn indicates the total intensity of pixel (i,j), Ii,jo indicates the original pixel intensity and ni,j indicates the added noise intensity. Such a noise is usually caused by transmission error, and it may make pixel intensity abnormally fluctuate. Such a fluctuation is often utilized by many filtering methods.

As we know, linear filtering cannot effectively remove impulse noise because it may mistakenly detect object edge as noise region. Just for overcoming this weakness, some nonlinear technologies [15], [2], [24], [10], [3], [16] and neural filtering method [37] are specially developed. Like most methods, these also consist of two basic steps, namely noise detection and pixel replacement with an estimated value. However, these methods are only effective for removing impulse noise. For the removal of additional Gaussian noise, they seldom work well.

In addition to these above, wavelet transform (WT) [18] and partial differential equations (PDEs) with partial derivative estimation are also powerful tools for removing noise. The WT-based methods are often categorized into two classes, namely attenuation and selection. Many WT-based ones are developed for removing white Gaussian noise [19], [25], [26]. Moreover, for PDEs, the classical heat equation [30] and some nonlinear diffusion algorithms [23], [36], [12], [7] are also frequently used for the removal of additional Gaussian noise. However, the two tools have a same application limitation, namely like linear technologies, they are also inefficient for the removal of impulse noise.

Seldom, an image only contains single noise (Gaussian or impulse noise), and it is often contaminated by more than one type of noise, such as mixed noise. The mixed noise is often caused in some complex environment, for example, an image with Gaussian noise is transmitted through a disturbed communication channel. For the existing noise image filtering technologies, most of them are specially proposed for removing single noise [29], [31], [2], [10], [3], [16], [37], [17], and some others are presented for the mixed noise removal, such as the local image statistic filtering approach [6], the median-based SD-ROM filter [1], and the fuzzy noise filter [22]. These technologies mentioned above can only remove low-intensity mixed noise, and when they are applied to high-intensity noise, the filtering performances often heavily decline.

This paper gives a study on the removal of mixed noise using pulse coupled neural networks (PCNNs). The initial PCNN model proposed by Echorn originates from the observation of synchronous pulses in cat visual cortex [4]. Lindblad discusses image processing technologies of PCNN [13], and Johnson systematically describes some classical PCNN models and their typical applications in [9]. Moreover, Ranganath and Kuntimad develop several image processing methods [28] using modified PCNNs, such as object detection [27] and image segmentation [11]. In addition, Lindblad also discusses the pinpoint differences as well as similarities between PCNN and wavelet transform in 2D data processing [14]. Recently, various applications of PCNN are proposed, such as the pattern recognition method [20] by Muresan, the image shadow removal approach [8] by Gu, the noise filtering technology [17] by Ma, the image thinning algorithm [34] by Shang, and the intersecting cortical model (ICM) for special image processing [5] by Ekblada.

However, these traditional PCNNs are only useful for removing single noise [37], [17]. To develop the mixed noise removal of PCNN, this paper constructs a two-channel parallel filter by proposing a weighted-linking PCNN model that originates from [9], [27], [20], [8], [34]. Like [27], [17], this filter also needs to iteratively run, so we design a special stopping condition for determining when the two-channel PCNN filtering finishes. In this filter, each channel consists of two serial PCNNs, and each PCNN iteratively detects and removes noise using neuron pulses and pixel intensity variation, until the given stopping condition is satisfied. In addition to these, to obtain good filtering performance, these channel outputs are fused together using an optimization strategy.

The remainder of this paper is organized as follows. Section 2 introduces the pulse coupled neuron (PCN) model of the proposed network. Section 3 presents how to construct a two-channel filter using four PCNNs, and choose suitable parameters for them. Section 4 exhibits experimental results and comparisons. Finally, some conclusions are drawn in Section 5.

Section snippets

Weighted-linking PCNN model

PCNN, a well-known class of neural networks, has many advantages, such as fast parallel processing capability and one-to-one relationship between neurons and image pixels. It can conveniently process image by manipulating its neurons. These advantages make it quite attractive to image processing, as a result, many classical PCNN-based applications have been found. For noise removal, some initial algorithms [28], [27], [17] have been proposed, but limited by the adopted PCNN models, they are

Noise filtering using weighted-linking PCNNs

For image filtering, how to detect noise pixel is a crucial problem. Once it is determined, how to remove it is another problem. Since additional Gaussian noise and impulse noise conform to different distributions, we have to design a new filter, consisting of four weighted-linking PCNNs, to process mixed noise. Fig. 3 shows the coarse structure of such a proposed filter.

As shown in Fig. 3, this filter consists of four PCNNs, two for Gaussian noise, and the others for impulse noise. Networks N2

Experiments of testing and evaluation

In this section, two classical images and a PC with 800 Hz CPU are used in the experiments. These experiments mainly consist of two parts, namely testing the proposed algorithm and comparing it with some others. Throughout this section, p (0p1) denotes the intensity of impulse noise and σ (0σ1) denotes the standard variance of additional Gaussian noise.

Generally, filtering performance can be evaluated by NMSE (Eq. (13)) and peak signal-to-noise ratio (PSNR). Herein, PSNR is formulated byPSNR(

Conclusions

To remove mixed noise in images, this paper proposes a weighted-linking PCNN model by (i) extending the linking input, (ii) defining an universal weighted-linking rule, (iii) redefining the real-time pulse threshold, (iv) modifying the computation rule of activity strength and (v) designing the pixel variation rule of neuron. Based on such a model, a two-channel parallel filter is constructed. By choosing suitable parameters, it can effectively remove single impulse noise (p>0.0,σ=0.0) and

Mr. Luping Ji received his B.S. degree from Beijing Institute of Technology, Beijing, China, in July 1999 and M.S. degree from University of Electronic Science and Technology of China, Chengdu, China, in April 2005. Currently, he is a Ph.D. student in the Computational Intelligence Laboratory of University of Electronic Science and Technology of China, Chengdu, China. His research interests include Neural Networks and Pattern Recognition.

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    Mr. Luping Ji received his B.S. degree from Beijing Institute of Technology, Beijing, China, in July 1999 and M.S. degree from University of Electronic Science and Technology of China, Chengdu, China, in April 2005. Currently, he is a Ph.D. student in the Computational Intelligence Laboratory of University of Electronic Science and Technology of China, Chengdu, China. His research interests include Neural Networks and Pattern Recognition.

    Dr. Zhang Yi received his Ph.D. degree in mathematics from the Institute of Mathematics, The Chinese Academy of Science, Beijing, China, in 1994. Currently, he is a Professor in the Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China. He is the author of the book Convergence Analysis of Recurrent Neural Networks and coauthor of the book Neural Networks: Computational Models and Applications. His current research interests include Neural Networks and Data Mining.

    This work was supported by National Science Foundation of China under Grant 60471055 and Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20040614017.

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