基于l_(2,1)范数原子选择的图像分块稀疏重构
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摘要
针对图像压缩采样中原子的选择规则难以确定的问题,在改进的正交匹配追踪算法的基础上提出了一种基于l_(2,1)范数的原子选择方式。l_(2,1)范数的原子选择方式考虑了原子间的相关性,剔除了干扰原子,选择出了代表性原子。将所提方法用于图像分块重构,算法以图像进行分块,利用l_(2,1)范数选择对图像块支撑集进行筛选,增强块特征的判别性,提高原子的稀疏度,最终提高图像重构的准确率和速率。实验结果表明,相同条件下在保证重建速度的同时,所提新方法提高了图像重构精度。
In order to solve the problem of selecting atoms for image compressed samples automatically,this paper proposed a new l_(2,1)-norm atomic selection method. The proposed method took into account the correlation between the atoms,eliminated the interference of atoms and selected a representative of the atomic. Image reconstruction based on image segmentation and l_(2,1)-norm selection. This algorithm divided image into blocks,and filtered the image blocks supporting set by the l_(2,1)-norm selection which enhanced the discriminant of block features,improved the sparsity of atoms,and ultimately improved the accuracy and speed of image reconstruction. The simulation results show that the reconstruction accuracy can be improved with the same condition.
In order to solve the problem of selecting atoms for image compressed samples automatically,this paper proposed a new l_(2,1)-norm atomic selection method. The proposed method took into account the correlation between the atoms,eliminated the interference of atoms and selected a representative of the atomic. Image reconstruction based on image segmentation and l_(2,1)-norm selection. This algorithm divided image into blocks,and filtered the image blocks supporting set by the l_(2,1)-norm selection which enhanced the discriminant of block features,improved the sparsity of atoms,and ultimately improved the accuracy and speed of image reconstruction. The simulation results show that the reconstruction accuracy can be improved with the same condition.
引文
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[20]Shi Xiaoshuang,Yang Yujiu,Guo Zhenhua,et al.Face recognition by sparse discriminant analysis via joint l2,1-norm minimization[J].Pattern Recognition,2014,47(7):2447-2453.
[21]Sun Liang,Liu Jun,Chen Jianhui,et al.Efficient recovery of jointly sparse vectors[C]//Proc of International Conference on Neural Information Processing Systems.[S.l.]:Curran Associates Inc.,2009:1812-1820.
[2]Tropp J A,Gilbert A C,Strauss M J.Algorithms for simultaneous sparse approximation,part I:greedy pursuit[J].Signal Processing,2006,86(3):589-602.
[3]Figueiredo M A T,Nowak R D,Wright S J.Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics on Signal Processing,2008,1(4):586-597.
[4]Parikh N,Boyd S.Proximal algorithms[J].Foundations&Trends in Optimization,2014,1(3):127-239.
[5]Efron B,Hastie T,Johnstone I,et al.Least angle regression[J].Annals of Statistics,2004,32(2):407-451.
[6]Donoho D L,Tsaig Y,Drori I,et al.Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit[J].IEEE Trans on Information Theory,2012,58(2):1094-1121.
[7]刘学文,肖嵩,王玲,等.迭代预测正交匹配追踪算法[J].信号处理,2017,33(2):178-184.(Liu Xuewen,Xiao Song,Wang Ling,et al.Iterative predictive orthogonal matching pursuit algorithm[J].Signal Processing,2017,33(2):178-184.)
[8]Needell D,Vershynin R.Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit[J].IEEE Journal of Selected Topics on Signal Processing,2010,4(2):310-316.
[9]Needell D,Tropp J A.Co Sa MP:iterative signal recovery from incomplete and inaccurate samples[J].Applied&Computational Harmonic Analysis,2009,26(3):301-321.
[10]Dai W,Milenkovic O.Subspace pursuit for signal reconstruction[J].IEEE Trans on Information Theory,2009,55(5):2230-2249.
[11]Do T T,Gan Lu,Nguyen N,et al.Sparsity adaptive matching pursuit algorithm for practical compressed sensing[C]//Proc of Asilomar Conference on Signals,Systems and Computers.Piscataway,NJ:IEEEPress,2009:581-587.
[12]田金鹏,刘小娟,郑国莘.一种变步长稀疏度自适应子空间追踪算法[J].自动化学报,2016,42(10):1512-1519.(Tian Jinpeng,Liu Xiaojuan,Zheng Guoshen.A variable step size sparsity adaptive subspace tracking algorithm[J].Journal of Automation,2016,42(10):1512-1519.)
[13]刘亚新,赵瑞珍,胡绍海,等.用于压缩感知信号重建的正则化自适应匹配追踪算法[J].电子与信息学报,2010,32(11):2713-2717.(Liu Yaxin,Zhao Ruizhen,Hu Shaohai,et al.Regularized adaptive matching pursuit algorithm for compressed sensing signal reconstruction[J].Journal of Electronics and Information,2010,32(11):2716-2717.)
[14]吴迪,王奎民,赵玉新,等.分段正则化正交匹配追踪算法[J].光学精密工程,2014,22(5):1395-1402.(Wu Di,Wang Kuimin,Zhao Yuxin,et al.Segmented regularized orthogonal matching pursuit algorithm[J].Optical Precision Engineering,2014,22(5):1395-1402.)
[15]唐朝伟,王雪锋,杜永光.一种稀疏度自适应分段正交匹配追踪算法[J].中南大学学报:自然科学版,2016,47(3):784-792.(Tang Chaowei,Wang Xuefeng,Du Yongguang.A sparse adaptive piecewise orthogonal matching pursuit algorithm[J].Journal of Central South University:Natural Science Edition,2016,47(3):784-792.)
[16]Yao Shihong,Sangaiah A K,Zheng Zhigao,et al.Sparsity estimation matching pursuit algorithm based on restricted isometry property for signal reconstruction[M]//Future Generation Computer Systems.Berlin:Springer,2017.
[17]Onose A,Dumitrescu B.Adaptive matching pursuit using coordinate descent and double residual minimization[M].[S.l.]:Elsevier North-Holland Inc.,2013.
[18]Nie Feiping,Huang Heng,Cai Xiao,et al.Efficient and robust feature selection via joint l2,1-norms minimization[C]//Proc of International Conference on Neural Information Processing Systems.[S.l.]:Curran Associates Inc.,2010:1813-1821.
[19]Yang Yi,Shen Hengtao,Ma Zhigang,et al.l2,1-norm regularized discriminative feature selection for unsupervised learning[C]//Proc of International Joint Conference on Artificial Intelligence.[S.l.]:AAAI Press,2011:1589-1594.
[20]Shi Xiaoshuang,Yang Yujiu,Guo Zhenhua,et al.Face recognition by sparse discriminant analysis via joint l2,1-norm minimization[J].Pattern Recognition,2014,47(7):2447-2453.
[21]Sun Liang,Liu Jun,Chen Jianhui,et al.Efficient recovery of jointly sparse vectors[C]//Proc of International Conference on Neural Information Processing Systems.[S.l.]:Curran Associates Inc.,2009:1812-1820.