本論文針對稀疏表現超解析度演算法提出平行化設計演算法做改良。為了能夠減少原本演算法的處理時間，對於原本運算步驟依照平行化的概念使用統一計算架構(Compute Unified Device Architecture)，考量硬體的特性和限制做演算法的調整和修正藉以達成減少運算時間的目標。另外在平行化演算法中，針對計算稀疏係數的步驟透過使用最少絕對收縮和算子選擇(Least Absolute Shrinkage and Selection Operator)的方法來加速演算法的執行時間。此方法計算較為容易，也能比本來方法的執行時間更快。實驗結果顯示將原本演算法透過平行化的設計概念實現在影像品質標準改善程度不變的前提下執行時間結果能夠加速7.3倍，透過使用調整過的最少絕對收縮和選擇算子方法的執行時間加速結果為13.9倍。對於透過平行化設計的演算法和本來演算法針對執行時間做比較，並將使用調整過的最少絕對收縮和選擇算子方法跟原本演算法透過不同的影像品質評斷標準像是峰值信噪比(PSNR)、特徵相似性(FSIM)以及結構相似性(SSIM)等做處理結果比較。

This thesis proposes a parallel computing design algorithm for image Super Resolution with sparse representation. To reduce the algorithm’s processing time, we use the Computing Unified Device Architecture based on the concept of parallel computing. With the consideration on hardware’s limitation, we modified the original algorithm’s computing steps to achieve the goal for decreasing the processing time. In parallel computing design algorithm, we consider the least absolute shrinkage and selection operator (LASSO) method to speed up the processing time in finding the sparse coefficient. The proposed method is easy for operating on the GPU hardware computing. Compare with the original method implemented on Matlab, the GPU based algorithm can achieve 7.3 times faster than original through the parallel computing design concept. We replace the computing for sparse coefficient through the method of modified LASSO and the processing time can get 13.9 faster than original’s execution time. For the image quality, we adapt some image quality assessment standard such as the Pick Signal to Noise Ratio (PSNR), the Feature Similarity (FSIM), and the Structure Similarity (SSIM).

[1]J. Sun; Z.B. Xu; H.Y. Shum, “Image Super-Resolution Using Gradient Profile Prior” in IEEE Computer Vision and Pattern Recognition Conf., CVPR 2008, Anchorage, AK, pp. 1 - 8, June 2008
[2]W.T. Freeman; E.C. Pasztor, “Learning Low-Level Vision” in IEEE Computer Vision Conf., ICCV 1999, Vol. 2, Kerkyra, pp. 1182 - 1189, Apr. 1999
[3]S.T. Roweis and L.K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science, vol. 290, no. 5500, pp.2323 - 2326, Dec. 2000
[4]S.B. Chen and D. Donoho, “Basis Pursuit” in Signals Systems and Computers 1994 Conference Record of the Twenty-Eighth Conference, Volume:1, Asilomar, pp. 41 - 44, Oct. 1994
[5]R. Tibshirani, “Regression Shrinkage and Selection via the Lasso: A Retrospective,” J. Roy. Statist. Soc., Ser. B, Vol. 73, no. 3, pp. 273 – 282, June 2011
[6]Z. Wang; A.C. Bovik ; H.R.Sheikh and E.P. Simoncelli ,“Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600 - 612, Apr. 2004
[7]L. Zhang, D. Zhang and X. Mou , “FSIM: A Feature Similarity Index for Image Quality Assessment,” Image Processing, IEEE Transactions on Volume: 20 , no. 8 , pp. 2378- 2386, Aug. 2011
[8]J. Yang, J. Wright, T.S. Huang, and Y. Ma, “Image Super-Resolution Via Sparse Representation,” IEEE transactions Image Proceedings, Vol. 19. No.11, pp. 2861 - 2873 , Nov. 2010
[9]H. Lee , A. Battle , R. Raina and A. Y. Ng, “Efficient sparse coding algorithms,” Proc. Adv. Neural Inf. Process. Syst., pp.801 - 808 ,2007
[10]J. Yang, Z.W. Wang, Z. Lin, S. Cohen, T. Huang, “Coupled Dictionary Training for Image Super-Resolution,” Image Processing, IEEE Transactions on Volume: 21, no. 8, pp. 3467 – 3478, Aug. 2012
[11]R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. Roy. Statist. Soc., Ser. B, Vol. 58, no. 1, pp.267 - 288, Oct. 1994
[12]W. J. Fu , “Penalized Regressions: The Bridge versus the Lasso,” Journal of Computational and Graphical Statistics, Vol. 7, No. 3, pp. 397-416, Sep. 1998
[13]J. M. Cecilia, J. M. García and M. Ujaldón, “The GPU on the Matrix-Matrix Multiply: Performance Study and Contributions” in Advances in Parallel Computing, Vol. 19, pp. 331-340, Apr. 2010
[14]K.Z. Sun, J.D. Li and S.Y. Xu, “GPU-Accelerated Non-Local Means Super-Resolution Reconstruction” in Proceedings of the 3rd International Conf. on Multimedia Technology, ICMT 2013, GuangZhou, China, pp. 1242-1249, Nov. 2013
[15]X.F. Wu, H. Xiang and P. Lu, “A GPU Accelerated Algorithm for Compressive Sensing Based Image Super-Resolution” in Digital Media and Digital Content Management, DMDCM 2011 Workshop, pp:198-202, May 2011
[16]H. Chang, D.Y. Yeung and Y. Xiong,“Super-Resolution through Neighbor Embedding.” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2004, vol.1, Washington, DC, USA, pp.275-282, June 2004
[17]X. Li and M. Orchard, “New Edge-Directed Interpolation,” IEEE Trans. on Image Processing, vol. 10, no. 10, pp. 1521-1527, Oct. 2001