LettersDenoising MMW image using the combination method of contourlet and KSC shrinkage☆
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:where and are, respectively, the n-dimensional natural image data and the m-dimensional sparse coefficients (usually ). denotes the feature basis vectors and the symbol 〈·〉 denotes the mean. and 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 . 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)
Denoising natural images based on a modified sparse coding algorithm
Appl Math Comput
(2008)Non-negative sparse coding shrinkage for image denoising using normal inverse Gaussian density model
Image Vision Comput
(2008)- et al.
Active MMW focal plane imaging system
Pierre Kornprobst: Mathematical problems in image processing
(2002)
Cited by (5)
Dual stage Bayesian network with dual-tree complex wavelet transformation for image denoising
2020, Journal of Engineering Research (Kuwait)A novel mathematical model based medical image segmentation methodology: Theoretical analysis and applications
2015, Journal of Medical Imaging and Health InformaticsDenoising natural images using fast multiscale directional filter banks
2015, International Journal of Tomography and SimulationFast multiscale directional filter bank-based speckle mitigation in gallstone ultrasound images
2014, Journal of the Optical Society of America A: Optics and Image Science, and VisionThe nonlocal sparse reconstruction algorithm by similarity measurement with shearlet feature vector
2014, Mathematical Problems in Engineering
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).