1.School of Information Science and Engineering, Central South University, Changsha 410083 2.Engineering Research Center of Electric Power and Traffic Safety Monitoring and Control and Energy Conservation Technology, Ministry of Education, Changsha University of Science and Technology, Changsha 410004 3.School of Sciences, Beijing University of Civil Engineering and Architecture, Beijing 100044
Abstract To obtain the sparsest representation of an image using a redundant dictionary is NP-hard, and the existing sub-optimal algorithms for solving this problem such as matching pursuit (MP) are highly complex. An image sparse decomposition algorithm based on multi-population discrete differential evolution for multi-component Gabor dictionaries is proposed. Three sub-populations are adopted to search the best matching atoms in different sub-dictionaries, and the correlation coefficient is used to solve overlap-matching in updating process of residual image. To maintain the population diversity, several mutation operators are employed to generate the offspring population in the proposed algorithm. Experimental results show that the sparse approximation performances of the proposed algorithm are comparable with fast matching pursuit (FMP) algorithm. Meanwhile, the computation speed is improved. The proposed algorithm obtains competitive performance compared with other sparse representation methods based on evolution algorithm. Finally, the rationality of the parameters setting in the proposed algorithm is verified by result analysis.
[1] Mallat S G, Zhang Z F. Matching Pursuits with Time-Frequency Dictionaries. IEEE Trans on Signal Processing, 1993, 41(12): 3397-3415 [2] Wright J, Yang A Y, Ganesh A, et al. Robust Face Recognition via Sparse Representation. IEEE Trans on Pattern Analysis and Machine Intelligence, 2009, 31(2): 210-227 [3] Yang J C, Wright J, Huang T S, et al. Image Super-Resolution via Sparse Representation. IEEE Trans on Image Processing, 2010, 19(11): 2861-2873 [4] Gan T, He Y M. Scalable Image Coding Based on Sparse Decomposition. Acta Electronica Sinica, 2010, 38(1): 156-160 (in Chinese) (甘 涛,何艳敏.基于稀疏分解的可伸缩图像编码.电子学报, 2010, 38(1): 156-160) [5] Figueras i Ventura R M, Vandergheynst P, Frossard P. Low-Rate and Flexible Image Coding with Redundant Representations. IEEE Trans on Image Processing, 2006, 15(3): 726-739 [6] Sun Y B, Xiao L, Wei Z H, et al. Sparse Representations of Images by a Multi-component Gabor Perception Dictionary. Acta Automatica Sinica, 2008, 34(11): 1379-1387 (in Chinese) (孙玉宝,肖 亮,韦志辉,等.基于Gabor感知多成份字典的图像稀疏表示算法研究.自动化学报, 2008, 34(11): 1379-1387) [7] Lobo A P, Loizou P C. Voiced/Unvoiced Speech Discrimination in Noise Using Gabor Atomic Decomposition // Proc of the IEEE International Conference on Acoustics, Speech, and Signal Processing. Hong Kong, China, 2003, I: 820-823
[8] Davis G, Mallat S, Avellaneda M. Adaptive Greedy Approximations. Constructive Approximation, 1997, 13(l): 57-98 [9] Jaggi S, Karl W C, Mallat S, et al. High Resolution Pursuit for Feature Extraction. Applied and Computational Harmonic Analysis, 1998, 5(4): 428-449 [10] Blumensath T, Davis M E. Gradient Pursuits. IEEE Trans on Signal Processing, 2008, 56(6): 2370-2382 [11] Yin Z K, Shao J, Vandergheynst P. MP Based Signal Sparse Decomposition with FFT. Journal of Electronics & Information Technology, 2006, 28(4): 614-618 (in Chinese) (尹忠科,邵 君,Vandergheynst P.利用FFT实现基于MP的信号稀疏分解.电子与信息学报, 2006, 28(4): 614-618) [12] Wang Z L, He H J, Wang J Y, et al. Fast Algorithm for Image MP Sparse Decomposition Based on FHT and Core Dictionary. Journal of the China Railway Society, 2012, 34(9): 51-57 (in Chinese) (王在磊,和红杰,王建英,等.基于核心原子库和FHT的图像MP稀疏分解快速算法.铁道学报, 2012, 34(9): 51-57) [13] Wang J Y, Yin Z K, Zhang C M. Sparse Decomposition and Preliminary Applications of Signals and Images. Chengdu, China: Southwest Jiaotong University Press, 2006 (in Chinese) (王建英,尹忠科,张春梅.信号与图像的稀疏分解及初步应用.成都:西南交通大学出版社, 2006) [14] Feng X Q, He T J. Fast Matching Pursuit for Traffic Images Using Differential Evolution. Journal of Harbin Institute of Technology, 2010, 17(2): 193-198 [15] Chen C, Liang J J, Qu B Y, et al. Using Dynamic Multi-swarm Particle Swarm Optimizer to Improve the Image Sparse Decomposition Based on Matching Pursuit // Proc of the 9th International Conference on Intelligent Computing. Nanning, China, 2013: 587-595 [16] Sun Y B. Sparse Representations of Images and Its Application to Inverse Problems in Image Processing. Ph.D Dissertation. Nanjing, China: Nanjing University of Science and Technology, 2010 (in Chinese) (孙玉宝.图像稀疏表示模型及其在图像处理反问题中的应用.博士学位论文.南京:南京理工大学, 2010) [17] Wang Y, Cai Z X. Constrained Evolutionary Optimization by Means of (μ+λ)-Differential Evolution and Improved Adaptive Trade-Off Model. Evolutionary Computation, 2011, 19(2): 249-285 [18] Deng C Z, Cao H Q. Multi-atoms Rapid Matching Pursuit Algorithm with Incoherent Sub-dictionary. Signal Processing, 2009, 25(4): 613-617 (in Chinese) (邓承志,曹汉强.非相干子字典多原子快速匹配追踪算法.信号处理, 2009, 25(4): 613-617) [19] Ronkkonen J, Kukkonen S, Price K V. Real-Parameter Optimization with Differential Evolution // Proc of the IEEE Congress on Evolutionary Computation. Edinburgh, UK, 2005, Ⅰ: 506-513
2014, Vol. 27 
