A Novel Image Super-resolution Reconstruction Algorithm based on Modified Sparse Representation

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1 , pp A Novel Image Super-resolution Reconstruction Algorithm based on Modified Sparse Representation Liqiang Hu, Chaofeng He Shijiazhuang Tiedao University, Shijiazhuang, Hebei , China Abstract. This paper proposes a novel image super-resolution reconstruction algorithm based on modified sparse representation. Compression perception is in recent years the rise of a new basic compression technology in the world. Different with the traditional compression principle, the theory broke through the classic Nyquist sampling theorem, points out that as long as the signal is compressible. In order to overcome the traditional image compression perception in baseband using orthogonal basis or fixed dictionary as sparse transform to the low quality of the basic image reconstruction and adaptability is not strong, the author according to the ideas of the polyatomic library adaptive learning, and image sparse coding model is established. It is obtained by three methods of sparse representation of the sparse coefficient has the obvious sparse, meet the conditions of compression perception. But from the point of sparse effect using DFT transformation matrix and DTC transformation matrix to obtain the coefficient of sparse is achieved. The experiment shows the effectiveness of the methodology. Keywords: Image Super-resolution, Reconstruction, Algorithm, Modified Sparse Representation, Image Processing. 1 Introduction Image super-resolution refers to the use of one or more of low resolution image, as through the corresponding algorithm to obtain the clear image of the high resolution image. These images are low resolution observation different imaging of the same scene, that subpixel level displacement between them, namely each image contains different information, so it can be worth more than any a high resolution image of low resolution image quality. Obviously, the low resolution image registration problem is the key of image super-resolution reconstruction, registration accuracy directly affect the effect of reconstruction. Super-resolution image reconstruction generally includes three steps: registration or basic motion estimation and interpolation and recovery. The interpolation refers to determine each LR images each pixel corresponding position in the HR image. The three step operation can simultaneously or separately, depending on the reconstruction algorithm adopted. If separately, the LR image motion estimation first conducted to calculate the sequence of sub pixel accuracy between the relative displacements and then use irregular interpolation algorithm from a series of uneven spatial distribution of the LR image sequence HR image interpolation to obtain uniform distribution grid, ISSN: ASTL Copyright 2016 SERSC

2 finally uses the image restoration algorithm to remove the illustrations as blur and noise effect. In actual imaging, dislocation line array on the scanning direction like yuan, dislocation in core array direction as yuan. A scan with online column direction staggered half like two images, the image on the scanning direction by controlling the integration time to determine the oversampling ratio, and the scanning velocity and the integral time to determine the size of the dislocation. In order to overcome the traditional image compression perception in baseband using orthogonal basis or fixed dictionary as sparse transform to the low quality of the basic image reconstruction and adaptability is not strong, the author according to the ideas of the polyatomic library adaptive learning, and image sparse coding model is established. The model obtained from iterative reconstruction process in the middle of the image study redundant dictionary, make full use of the atom and the dictionary for reconstruction of the image correlation, thus obtained the ideal image sparse coding. Use the image in the dictionary with sparse this prior knowledge, by solving related nonlinear optimization problem can be rebuilt out high quality images. 2 The Super-resolution Reconstruction Review Super-resolution reconstruction technology belongs to a part of the image fusion technology. The meaning of image fusion technology is to make correlation and are highly complementary in many images useful information together to produce the image (or sequence) to carry more information and to be able to make up for the limitations of the original observations carrying information. Before analyzing the basic procedure of the SR, we review the imaging process as the follows. L D* B* H N (1) As mentioned earlier, the SR recovery for pathological problems, solve the problem of effective method for the regularization method, which uses the image of the prior knowledge (local smoothing, edge to keep positive, energy etc.) to constrain the solution space. In other words, the SR reconstruction is an optimization problem to minimize the cost function. Most SR reconstruction method includes three steps: the registration, interpolation, and recovery. (2) As shown in the formula 2,we build the scenario. BAKER was deduced in theory of super-resolution image reconstruction technology limitations of three conclusions: (1) for a square point spread function (PSF) and integer multiples times increase, on the basis of the reconstruction of the reconstruction constraint condition to establish constraint equation is close to the irreversible, and zero space dimension increase multiples of a quadratic form. (2) even if the reconstruction constraint equation for other types of point spread function (PSF) may be reversible, the condition number of reconstruction constraint equations are still at least increased rapidly, at the rate of quadratic namely along with the increase of multiple, reconstruction constraint equation ill-posed getting worse. (3) larger enhancement factor, reconstruction constraint equations exist a large number of possible solutions. Adopting smoothness Copyright 2016 SERSC 163

3 prior conditions can help overcome the arbitrariness of solution, for sure. But affected by the prior condition of smoothness, reconstruction images may appear too smooth. Solving the type usually uses coordinate rotation method that also known as the alternating minimization method, the registration alternate estimated parameters and high resolution images. Due to the method in solving process, gradually to the local optimal solution is close to the original question of morbid degree can aggravate be constantly, lead to instability. In the later sections, we will show our methodology. Fig. 1. The Demonstration of the Super-resolution Reconstruction on Face Datasets 3 Sparse Representation and Dictionary Learning Compression perception is in recent years the rise of a new basic compression technology in the world. Different with the traditional compression principle, the theory broke through the classic Nyquist sampling theorem, points out that as long as the signal is compressible, can use a transformation matrix is not related the highdimensional signal measurement matrix projection to a low dimensional space, and can restore the original signal reconstruction algorithm as formula 3. (3) It can be solved by KSVD algorithm alternating update Y and the D type (2), the iteration process mainly includes: (1) under the current dictionary of X signal sparse decomposition, a lot of algorithms to realize such a sparse representation, such as the OMP, BP algorithm; (2) to update the atoms in the dictionary, its core is SVD algorithm. Among them, the optimization solution involves the SVD calculation of matrix, a large amount of calculation, largely limits the computation speed; When the image size, the number of iterations is larger, the calculation amount and great consumption of calculation, the time is too long, the practical value is limited by larger, at the same time, the algorithm cannot ensure the convergence. 164 Copyright 2016 SERSC

4 (4) It is obtained by three methods of sparse representation of the sparse coefficient has the obvious sparse, meet the conditions of compression perception. But from the point of sparse effect, using DFT transformation matrix and DTC transformation matrix to obtain the coefficient of sparse feature is not obvious, not fully reflect the characteristics of the original signal. This article uses the proximal gradient algorithm is optimized, the process of update and Y and D at the same time, the difference in the KSVD, alternating minimization method is used for the OLM update D and Y. Keep on D and the Y sub-problems have closed solution, reduce the complexity of the algorithm and each step iteration and the extrapolation is used to design at the same time, further speed up the convergence, reduced the number of the iterations, greatly shorten the operation time. The figure 2 shows the performance. Fig. 2. The Sparse Representation and Dictionary Learning Illustration Copyright 2016 SERSC 165

5 4 The Image Characteristics Compared with the traditional image feature extraction, this paper uses a massively parallel processing circuit, not only should have the edge on regional segmentation and edge detection features and angle, but also constantly in the timeline will spell out the target these areas connection of local image, and extract geometric characteristic and the connection relationship. Every moment in the scan images were increased, as while constantly from the characteristics of the image extracted enough to identify the target state of SEC and parts, identification system will no longer continue to scan the whole target. In the edge of the image are extracted, the selection of threshold is good or not directly affect the speed of edge detection can choose the first layer of the wavelet decomposition image threshold for all average grey value, the second floor of the threshold for the front half, so on also can choose the image grey value of the maximum half of the first layer of the wavelet decomposition image threshold, the other so on. The formula 5 show the proposed methodology. (5) 5 Summary and Conclusion This paper proposes a novel image super-resolution reconstruction algorithm based on modified sparse representation. Super-resolution image reconstruction generally includes three steps: registration or basic motion estimation and interpolation and recovery. The interpolation refers to determine each general LR images each pixel corresponding position in the HR image. The three step operation can simultaneously or separately, depending on the reconstruction algorithm adopted. If separately, the LR image motion estimation first conducted to calculate the sequence of sub pixel accuracy between the relative displacements and then use irregular interpolation algorithm from a series of uneven spatial distribution. By integrating the principle core characteristics of the sparse presentation, we achieve a better methodology on the issues that will be meaningful. References 1. Dong, C.: Learning a deep convolutional network for image super-resolution. European Conference on Computer Vision. Springer International Publishing, Villena, S.: Bayesian combination of sparse and non-sparse priors in image super resolution. Digital Signal Processing 23.2 (2013): Kwon, Y.: Efficient learning of image super-resolution and compression artifact removal with semi-local Gaussian processes. IEEE transactions on pattern analysis and machine intelligence 37.9 (2015): Copyright 2016 SERSC

6 4. Bevilacqua, M.: Single-image super-resolution via linear mapping of interpolated selfexamples. IEEE Transactions on image processing (2014): Akhtar, N., Shafait, F., Mian, A.: Sparse spatio-spectral representation for hyperspectral image super-resolution. European Conference on Computer Vision. Springer International Publishing, Zeng, X., Yang, L.: A robust multiframe super-resolution algorithm based on halfquadratic estimation with modified BTV regularization. Digital Signal Processing 23.1 (2013): Zhu, Y.: Modeling deformable gradient compositions for single-image super-resolution. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Liu, H.-c., Li, S.-t., Yin, H.-t.: Infrared surveillance image super resolution via group sparse representation. Optics Communications 289 (2013): Wang, H., Wang, J.: An Effective Image Representation Method Using Kernel Classification. IEEE International Conference on Tools with Artificial Intelligence IEEE, 2014: Yan, F., Iliyasu, A., Jiang, Z.: Quantum Computation-Based Image Representation, Processing Operations and Their Applications. Entropy 16.10(2014): Seo, D., Ho, J., Vemuri, B. C.: Covariant Image Representation with Applications to Classification Problems in Medical Imaging. International Journal of Computer Vision 116.2(2015):1-20. Copyright 2016 SERSC 167