Gradient Projection with Approximate L-0 Norm Minimization for Sparse Reconstruction in Compressed Sensing

doi:10.3390/s18103373

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	Gradient Projection with Approximate L-0 Norm Minimization for Sparse Reconstruction in Compressed Sensing
	Wei, Ziran 1,2,3; Zhang, Jianlin 1; Xu, Zhiyong 1; Huang, Yongmei 1; Liu, Yong 2; Fan, Xiangsuo 1,2,3
刊名	SENSORS
	2018-10-09
卷号	18 期号:10 页码:3373
关键词	compressed sensing convex optimization L-0 norm gradient projection sparse reconstruction
ISSN号	1424-8220
DOI	10.3390/s18103373
文献子类	J
英文摘要	In the reconstruction of sparse signals in compressed sensing, the reconstruction algorithm is required to reconstruct the sparsest form of signal. In order to minimize the objective function, minimal norm algorithm and greedy pursuit algorithm are most commonly used. The minimum L-1 norm algorithm has very high reconstruction accuracy, but this convex optimization algorithm cannot get the sparsest signal like the minimum L-0 norm algorithm. However, because the L-0 norm method is a non-convex problem, it is difficult to get the global optimal solution and the amount of calculation required is huge. In this paper, a new algorithm is proposed to approximate the smooth L-0 norm from the approximate L-2 norm. First we set up an approximation function model of the sparse term, then the minimum value of the objective function is solved by the gradient projection, and the weight of the function model of the sparse term in the objective function is adjusted adaptively by the reconstruction error value to reconstruct the sparse signal more accurately. Compared with the pseudo inverse of L-2 norm and the L-1 norm algorithm, this new algorithm has a lower reconstruction error in one-dimensional sparse signal reconstruction. In simulation experiments of two-dimensional image signal reconstruction, the new algorithm has shorter image reconstruction time and higher image reconstruction accuracy compared with the usually used greedy algorithm and the minimum norm algorithm.
WOS关键词	SIGNAL RECOVERY
语种	英语
WOS记录号	WOS:000448661500201
内容类型	期刊论文
源URL	[http://ir.ioe.ac.cn/handle/181551/9370]
专题	光电技术研究所_光电工程总体研究室（一室）
作者单位	1.Institute of Optics and Electronics, Chinese Academy of Science, Chengdu; 610209, China; 2.School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu; 610054, China; 3.University of Chinese Academy of Sciences, Beijing; 100039, China
推荐引用方式 GB/T 7714	Wei, Ziran,Zhang, Jianlin,Xu, Zhiyong,et al. Gradient Projection with Approximate L-0 Norm Minimization for Sparse Reconstruction in Compressed Sensing[J]. SENSORS,2018,18(10):3373.
APA	Wei, Ziran,Zhang, Jianlin,Xu, Zhiyong,Huang, Yongmei,Liu, Yong,&Fan, Xiangsuo.(2018).Gradient Projection with Approximate L-0 Norm Minimization for Sparse Reconstruction in Compressed Sensing.SENSORS,18(10),3373.
MLA	Wei, Ziran,et al."Gradient Projection with Approximate L-0 Norm Minimization for Sparse Reconstruction in Compressed Sensing".SENSORS 18.10(2018):3373.