Elsevier

Neurocomputing

Volume 83, 15 April 2012, Pages 229-233
Neurocomputing

Letters
Denoising MMW image using the combination method of contourlet and KSC shrinkage

https://doi.org/10.1016/j.neucom.2011.11.003Get rights and content

Abstract

A new denoising method of milli-meter wave (MMW) image using contourlet and kurtosis based sparse coding (KSC) is proposed in this paper. KSC is a high-order statistical method and can efficiently extract image feature coefficients. Contourlet method has the decomposition property of orientation and the energy variation for images. Further, using the shrinkage threshold that is determined by the sparse prior distribution of feature coefficients extracted in the contourlet transform field, the unknown noise contained in MMW image can be reduced efficiently. In test, an artificial MMW image and a true MMW are respectively used to validate our method, further, compared this method with other denoising methods, the simulation results show this method proposed here can obtain the better quality of image restoration.

Introduction

The millimeter wave (MMW) image technology has received a lot of attention, but the MMW image obtained is of lower resolution and its quality is very worse, at the same time, much unknown noise is also added in the MMW imaging process, and this further makes the MMW image severely degenerated [1]. Currently, many image denoising methods have been developed, and the methods are usually divided into linear ones and non-linear ones, such as median filter [2], winner filter [2], wavelet filter [2], [3], contourlet filter [4], and the partial differential equations (PDEs) algorithm [5], etc., although the above-mentioned methods can denoising MMW images to some extent, the denoising results are still not satisfied only using one of these methods. In recent years, the sparse coding shrinkage (SCS) technique is explored and has been widely used in image processing fields [6], [7]. This denoising method considers the high-order statistical property of images, and can retain the image's edge information in degree. However, when using the SCS shrinkage method to denoise images, the noise variance must be known. While in MMW images, the noise variance is unknown. Therefore, it is ill-suited to denoise a MMW image only using SCS method. To solve this problem, the contourlet transform is used here, and it is easy to estimate the noise level in a sub-band image obtained by contourlet transform. Thus, the advantages of contourlet and SCS are combined in this paper, further, they are discussed in denoising MMW images.

Section snippets

The cost function

Referring to the classical SC algorithm [6], [7], the cost function of the kurtosis-based sparse coding (KSC) algorithm is constructed as follows:J(A,S)=12x,y[X(x,y)iai(x,y)si]2λ14i|kurt(si)|+λ2i[ln(si2σt2)]2where X=(x1,x2,,xn)T and S=(s1,s2,,sm)T are, respectively, the n-dimensional natural image data and the m-dimensional sparse coefficients (usually mn). A=(a1,a2,,am) denotes the feature basis vectors and the symbol 〈·〉 denotes the mean. λ1 and λ2 are positive constant

Contourlet transformation

To describe the singular information in images, Do et al. [9] proposed a contourlet transform. This transform offers a flexible multi-resolution and directional decomposition for images, since it allows for a different number of directions at each scale. This transform can embody an image's structure well, and the transform process can be simply generalized as three steps: (1) First, to catch all singular points in an image, the multi-scale decomposition is realized by using the Laplace pyramid

KSC shrinkage rule combined with contourlet transformation

Combined the advantages of KSC shrinkage and contourlet transformation, we conclude a new MMW image denoising method, called contourlet–KSCS here. The main denoising process is written as follows:

Step 1. The original MMW image, contaminated by much unknown noise, is first transformed by contourlet, accordingly, the low-pass sub-bands and high-pass sub-bands are obtained. For the high-pass sub-bands obtained in the first layer decomposition of contourlet, the Eq. (5) is used to estimated noise

Experimental results

To explore the contourlet–KSCS method, 10 clean natural images with the size 512×512 available from http://sipi.usc.edu/database/database.php, were selected randomly to learn KSC model. One of these 10 images called Lena and its noise version were respectively shown in Fig. 2(a) and (b). Each natural image was sampled randomly 5000 times by an 8×8 sub-window, and the input set with the size of 64×50000 was acquired and denoted by matrix X˜. X˜ was centered, whiten and processed by PCA, thus,

Conclusions

This paper introduces multi-scale transformation of contourlet into KSC shrinkage algorithm and proposes a new MMW image denoising method. Firstly, the MMW image containing much unknown noise is separated into some sub-bands with multi-scale and multi-direction using the contourlet transformation. For each high-pass sub-band in each decomposition layer, the noise level of the original MMW image can be estimated, at the same time, the KSC shrinkage rules are used to realize the local threshold

Li Shang received the B.Sc. degree and M.Sc. degree in Xi'an Mine University in June 1996 and June 1999, respectively. And in June 2006, she received the Doctor's degree in Pattern Recognition & Intelligent System in University of Science & Technology of China (USTC), Hefei, China. From July 1999 to July 2006, she worked at USTC, and applied herself to teaching. Now, she works at the department of Electronic information engineering, Suzhou Vocational University. At present, her research

References (9)

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Li Shang received the B.Sc. degree and M.Sc. degree in Xi'an Mine University in June 1996 and June 1999, respectively. And in June 2006, she received the Doctor's degree in Pattern Recognition & Intelligent System in University of Science & Technology of China (USTC), Hefei, China. From July 1999 to July 2006, she worked at USTC, and applied herself to teaching. Now, she works at the department of Electronic information engineering, Suzhou Vocational University. At present, her research interests include Image processing, Artificial Neural Networks and Intelligent Computing.

Pin-gang Su received the B.Sc. degree of Precision Instrument in HeFei University of Technology in June 1993. And in March 2003, he received M.Sc. degree of Electronics & Information in Shanghai Jiaotong University. From August 1993 to July 2003, he worked at Suzhou Kingda Group. Since July 2003, he works at the department of Electronic information engineering, Suzhou Vocational University. And he worked as visiting scholar at State key laboratory of MMW in Southeast University in 2007. At present, his research interests include MMW imaging system, MMW Image processing, MMW testing technology.

Tao Liu received the B.Sc. degree and M.Sc. degree in Hefei University of Technology in June 1987 and June 1999, respectively. And in June 2005, he received the Doctor's degree in Control Theory & Control Engineering in China University of Mining and Technology (CUMT), Xuzhou, China. Now, he works at the department of Electronic information engineering, Suzhou Vocational University. At present, his research interests include Artificial Immune System, Intelligent Computing and Image processing.

This work was supported by the National Nature Science Foundation of China (Grant no. 60970058), the Natural Science Foundation of Jiangsu Province of China (Grant BK2009131), the Innovative Team Foundation of Suzhou Vocational University (Grant no. 3100125), and the Suzhou Science and Technology Infrastructure Construction Projects (Grant no. SZS201009).

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