A new ISR method based on the combination of modified K-SVD model and RAMP algrithm☆
Introduction
The spatial resolution of an image is an important measurement criterion of the image׳s equality. In generally, an image׳s spatial resolution means the minimized size can be distinguished clearly, which can be measured commonly using the spatial pixel density (i.e. pixels per inch, ppi) [1], [2], [3]. The higher the image resolution is, the larger the spatial pixel density is, and the smaller the reflective detail size in an image is, as well as the richer the image׳s detail is. Therefore, high resolution (HR) images are very useful in image processing field today [6], [7], [8]. However, in the practical process of imaging, the imaging result is degraded by some factors, such as the imaging pattern, the nature weather condition, and the hardware devices et al, so, the observed image is in fact a Low Resolution (LR) one. To obtain the HR images from LR ones, the research of Image Super-resolution Reconstruction (denoted by ISR) has been an important subfield in image processing field at present [6], [7], [8], [9], [10]. The goal of ISR is to reconstruct the High Resolution (HR) image from a single or a series of low resolution images [11], [12], [13], [14], [15], [16], [17]. Currently, this ISR technology also has been used widely in image reconstruction and image compression, high definition digital TV, remote-sensing and radar images, medical diagnostics and so on [5], [6], [7], [8]. To this day, many ISR methods have been proposed [1], [2], [3], [4], [5], [6], [7], [8], and they are summarized mainly as frequency domain method and spatial domain method. But, the former׳s denoising capability is limited in application. Moreover, this method can not fuse the prior information of images, and it can not be constrained by regularized rules. Therefore, the latter׳s research work is mainly done now.
The published typical spatial domain based ISR methods are divided into mainly three classes, i.e., the interpolation based method, the reconstruction based method and the learning based method [2], [3], [4], [5], [6], [7], [8]. The first class methods are very simple. However, this class of methods can not introduce extra high frequency information, and the supposed prior model is usually unstable, so the interpolation efficiency is commonly bad [3]. The second methods first assume that LR images are obtained by making HR images geometry deformed, fuzzed and down-sampled, further, they utilize the fusion of multiple LR images to invert HR images. However, in this class of methods, the motion estimation and matching among frame images are very critical. But, the precise image matching relation is very difficult to obtain, moreover, with the increasing of the resolution multiple (commonly exceed 4 times), the matching relation with minor error will cause great degradation of images restored [18], [19], thus, the matching relation is invalid. The last methods are learning based ones [15], [16], [17], [18], which can obtain much more high-frequency information by training samples to learn the relation between LR image patches and HR image patches. At present, learning based ISR methods are thought as the hot research topics. Currently, typical learning based image ISR methods generally are summarized as samples based ones [19], [20], Local Linear Embedding based Manifold Learning (LLE-ML) methods [19], Neighbor Embedding (NE) methods [21], [22], K-Nearest Neighbor (K-NN) methods [21], Kernel ridge regression methods [23], wavelet coefficient dictionary methods [22], and sparse representation based methods [24], [25] and so on. Among these typical ones, sparse representation based methods are the most popular and many ones also has been developed in restoring LR image s [24], [25], [26], [27], [28], [29]. Sparse representation based theories can well solve many inverse problems existing in the fields of images. At present, among published sparse representation based algorithms, the K-means based Singular Value Decomposition (K-SVD) is such a typical one [30], [31], [32], [33], [34], [35], and it has been used successfully in restoring, denoising and inpainting images. This method algorithm is an iterative method that alternates between sparse coding of the examples based on the current dictionary, and a process of updating the dictionary atoms to better fit the data [30]. The update of the dictionary column is combined with an update of the sparse representations, and thereby accelerating convergence can be done [36]. This K-SVD algorithm is very flexible and can work with any pursuit method (e.g. basis pursuit or matching pursuit).
Currently, in the common K-SVD algorithm, the over-complete dictionary is trained by using Orthogonal Matching Pursuit (OMP), Regularized OMP (ROMP) [14], [15], [16], Stage-wise OMP (StOMP) [15], [16], Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) [6], Sparsity Adaptive Matching Pursuit (SAMP) [6], [17], [18], Regularized Adaptive Matching Pursuit (RAMP), et al., these algorithms are summarized as greedy matching pursuit ones [18], [42], [43], [44], [45]. However, algorithms of OMP, ROMP, StOMP and SP require in advance the sparsity of the original data to be known [18], at the same time, they also lack provable reconstruction quality [16], [37], [38], [39], [40], [41], [42]. The SAMP is effective in the case that the sparsity is unknown [6]. However, the SAMP method could not remove inappropriate atoms out once they were chosen [18]. The RAMP algorithm was proposed by Liu et al. [5] by combining the advantages of ROMP and SAMP. This method can approach the sparsity adaptively by accumulating a fixed unit of step size and adding the method of regularization to select the atoms again [5], [17], [18], and the selection of atoms in this method becomes more flexible.
In this paper, considering the advances of RAMP and K-SVD as well as the maximum sparsity of image feature coefficients, a modified K-SVD (M_K-SVD) denoising model is proposed and further used to implement the ISR task. This M_K-SVD model behaves better self-adaptively denoising property and almost independent of sparse priors. Here, LR images are first pre-processed by M_K-SVD model based on RAMP optimization process. Further, utilized the idea of ISR technique and LR and HR dictionaries, trained by M_K-SVD model based on RAMP, the ISR task can be implemented well [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52]. At the same time, in order to reduce the iteration time, LR dictionary and HR dictionary are also classed by using K-mean method. Then, using LR coefficients and HR dictionary learned, the HR image patches can be restored efficiently. In test, a simulation LR image and a real LR image called Millimeter Wave (MMW) image are respectively used to testify our image ISR method. Further, the validity of our method is also proved that it has better reconstruction efficiency than most of the available greedy algorithms, such as the basic K-SVD, ROMP, RAMP, and SAMP.
The remainder of this paper is organized as follows. Section 2 will restate relative greedy algorithms, such as ROMP, SAMP, RAMP and so on. Section 3 gives the description of basic K-SVD algorithm and the M_K-SVD denoising model respectively. Finally, some simulation experiments are discussed in Section 4 and some conclusions are obtained in Section 5.
Section snippets
Relative greedy algorithms
At present, the popular class of sparse recovery algorithms is based on the idea of iterative greedy pursuit, such as OMP, ROMP, StOMP, CoSaMP above mentioned. It is noted that the RAMP algorithm is the combined one of ROMP and SAMP algorithms, therefore, the ROMP, SAMP and RAMP algorithm are mainly discussed.
K-SVD algorithm description
K-SVD algorithm is flexible and works in conjunction with any pursuit algorithm [32], [33], [34], and it is designed to be a truly direct generalization of the K-Means [33], [34], [35], [36], [37], [38]. Currently, it is also taken for a typical sparse representation method based on dictionary learning. In this case, the small amount of signal values can be reconstructed accurately when the signal is sparse. Set to be the dictionary matrix with prototype signal atoms for columns, to be the
Learning HR and LR dictionaries
In test, several degenerated versions of Lena image and real MMW images were used. The original Lena image with 128×128 pixels and imaging object of MMW imaging system were shown in Fig. 1(a) and (d). First, for Lena image, the motion blur operator was used, namely, PSF function was simulated. Next, for the blurred results of PSF, the down sampling method and Gaussian mask method were utilized. Further, to get degraded greatly images, the Gaussian blur method was used, thus, artificial LR
Conclusions
A novel image super-resolution reconstruction method combining a modified K-SVD (denoted by M_K-SVD) model and the RAMP algorithm is proposed in this paper. To improve the quality of reconstructed images, before training LR dictionaries, much unknown noise existed in LR images are first preprocessed by M_K-SVD model. Then, the HR and LR dictionary pairs are learned respectively by using M_K-SVD model based on the RAMP optimized process. After obtaining LR and HR dictionaries, utilizing usual
Acknowledgments
This work was supported by two National Natural Science Foundation of China (Grant nos. 61373098 and 61370109), the grant from Natural Science Foundation of Anhui Province (No. 1308085MF85), and the Innovative Achievement Foundation of Soochow Vocational University (No. 2011SZDCC06).
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 Communication Technology, Electronic Information Engineering College, Suzhou Vocational
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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 Communication Technology, Electronic Information Engineering College, Suzhou Vocational University. At present, her research interests include Image processing, Artificial Neural Networks and Intelligent Computing.
Xin Wang received the B.Sc. degree in Zhejiang University, China in July 2011. From July 2011 to July 2013, he worked as a research assistant at the College of Computer Science and Technology, Zhejiang University. He is currently pursuing the Ph.D. degree at the School of computing science of Simon Fraser University in Canada, in the area of Social Network and Recommender Systems. At present, his research interests include Machine Learning, Pattern Recognition, Recommender Systems and Social Networks.
Yan Zhou received the B.Sc. degree and M.Sc. degree in China University of Geosciences in June 2003 and June 2006, respectively. She is currently pursuing the Ph.D. degree at the School of Electronics and Information Engineering of Soochow University, in the area of signal and information processing. From July 2006 to now, she works at the Department of Communication Technology, Electronic Information Engineering College, Suzhou Vocational University. At present, her research interests include Speech Signal Processing, Artificial Neural Networks and Intelligent Computing.
Zhanli Sun received the Ph.D. degree from the University of Science and Technology of China, in 2005. Since 2006, he has worked with The Hong Kong Polytechnic University, Nanyang Technological University, and National University of Singapore. Now, he is currently a Professor with School of Electrical Engineering and Automation, Anhui University, China. His research interests include Machine Learning, Pattern Recognition, and Image and Signal Processing.
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Preliminary version of this manuscript has been selected as one of the best papers in International Conference on Intelligent Computing (ICIC 2014), 2014 (Paper ID: 127) and sub-selected in the Neurocomputing journal.
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