压缩感知OMP算法下信号重建方法研究

Abstract

CLC Number:

O175.5

Min Fu,Jiajun Hao,Liejun Xie,Jinping Wang. Exact Support Recovery of Sparse Signals from Noisy Measurements[J].Acta mathematica scientia,Series A, 2021, 41(5): 1555-1565.

Trendmd

Figures/Tables 6

输入: 样本 ${\bf y}$ , 采样矩阵 $\Phi$ , 稀疏度K
步骤1(识别): $\Lambda^{k} = \mathop{\arg\max}\limits _{\Upsilon\in\Gamma\setminus \Lambda_{k-1}}\mid \langle \Phi_{\Upsilon}, r^{k-1}\rangle\mid$
步骤2(增加): $\Lambda_{k} = \Lambda_{k-1}\cup\Lambda^{k}$
步骤3(估计): ${\bf x}^{(k)} = \mathop{\arg\min}\limits_{{\rm supp}({\bf u}) = \Lambda_{k}}\parallel {\bf y}-\Phi {\bf u}\parallel_{2}$
步骤4(更新): ${\bf r}_{k} = {\bf y}-\Phi {\bf x}^{(k)}$
输出: 重建信号 ${\bf x}^{(K)}$ , 最优原子集 $\Lambda_{K}$

输入: 样本 ${\bf y}$ , 采样矩阵 $\Phi$ , 稀疏度K
步骤1(识别): $\Lambda^{k} = \mathop{\arg\max}\limits_{\Upsilon\in\Gamma\setminus \Lambda_{k-1}}\mid \langle \Phi_{\Upsilon}, r^{k-1}\rangle\mid$
步骤2(增加): $\Lambda_{k} = \Lambda_{k-1}\cup\Lambda^{k}$
步骤3(估计): ${\bf x}^{(k)} = \mathop{\arg\min}\limits_{{\rm supp}({\bf u}) = \Lambda_{k}}\parallel {\bf y}-\Phi {\bf u}\parallel_{2}$
步骤4(筛选): 若 $\parallel {\bf x}^{(k)}-{\bf x}^{(k-1)}\parallel_{2}\leq \parallel {\bf y}\parallel_{2}$ ,
是, 接着步骤5, 否则, 步骤1.
步骤5(更新): ${\bf r}_{k} = {\bf y}-\Phi {\bf x}^{(k)}$
输出: 输出信号 $x^{K}$ , 最优原子集 $\Lambda_{K}$

References 22

1	Dnoho D L . Compressed sensing. IEEE Trans Inf Theory, 2006, 52 (4): 1289- 1306 doi: 10.1109/TIT.2006.871582
2	Duarte M F , Davenport M A , Takhar D , et al. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 2008, 25 (2): 83- 91 doi: 10.1109/MSP.2007.914730
3	Candés E J , Tao T . The power of convex relaxation: Near-optimal matrix completion. IEEE Trans Inf Theory, 2010, 56 (5): 2053- 2080 doi: 10.1109/TIT.2010.2044061
4	Vasanawala S , Alley M , Hargresves B , et al. Improved pediatric MR imaging with compressed sensing. Radiology, 2010, 256 (2): 607- 616 doi: 10.1148/radiol.10091218
5	Candes E J , Romberg J , Tao T . Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory, 2006, 52 (2): 489- 509 doi: 10.1109/TIT.2005.862083
6	Rezaiifar Y, Krishnaprasad P S. Orthogonal Matching Pursuit: Recursive Function Approximation with Applications to Wavelet Decomposition[C]//Proceedings of 27th Asilomar Conference on Signals, Systems & Computers. Pacific Grove, CA: IEEE, 2002
7	Dnoho D L , Tsaig Y , Drori I , et al. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans Inf Theory, 2012, 58 (2): 1094- 1121 doi: 10.1109/TIT.2011.2173241
8	Needell D , Tropp J A . Iterative signal recovery from incomplete and inaccurate samples. Appl Comput Harmon Anal, 2009, 26 (3): 301- 321 doi: 10.1016/j.acha.2008.07.002
9	Dai W , Milenkovic O . Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans Inf Theory, 2009, 55 (5): 4316- 4332
10	Wang J , Kwon S , Shim B . Generalized orthogonal matching pursuit. IEEE Trans Signal Processing, 2012, 60 (12): 6202- 6216 doi: 10.1109/TSP.2012.2218810
11	李峰, 郭毅. 压缩感知浅析. 北京: 科学出版社, 2015
	Li F , Guo Y . Compression Perception Analysed. Beijing: Science Press, 2015
12	Foucart S, Rauhut H. A Mathematical Introduction to Compressive Sensing. Berlin: Springer-Verlag, 2013
13	Davenport A M , Wakin B M . Analysis of orthogonal matching pursuit using restricted isometry property. IEEE Trans Inf Theory. Theory, 2010, 56, 4395- 4401 doi: 10.1109/TIT.2010.2054653
14	Liu E , Temlyakov V . The orthogonal super greedy algorithm and applications in compressed sensing. IEEE Trans Inf Theory, 2012, 58 (4): 2040- 2047 doi: 10.1109/TIT.2011.2177632
15	Wang J , Kwon S , Shim B . Near optimal bound of orthogonal matching pursuit using restricted isometric constant. Eur J Adv Signal Processing, 2012, 8, 1874- 1890
16	Wang J , Shim B . On the recovery limit of sparse signals using orthogonal matching pursuit. IEEE Trans Signal Processing, 2012, 60 (9): 4973- 4976 doi: 10.1109/TSP.2012.2203124
17	Li J , Wang Q , Shen Y . Near optimal condition of OMP algorithm in recovering sparse siganl from noisy measuurement. Systems Engineering and Electronics, 2014, 25 (4): 547- 553 doi: 10.1109/JSEE.2014.00063
18	Maleh R . Improved RIP analysis of orthogonal matching pursuit. Computer Science, 2011, 3, 782- 794
19	Chang L H , Wu J Y . An improved RIP-based performance guarantee for the sparse signal recovery via orthogonal matching pursuit. IEEE Trans Inf Theory, 2014, 60 (9): 4973- 4976
20	Mo Q . A sharp restricted isometry constant bound of orthogonal matching pursuit. Mathematics, 2015, 2, 249- 262
21	Wen J , Zhou Z , Wang J , et al. A sharp condition for exact support recovery with orthogonal matching pursuit. IEEE Trans Signal Processing, 2017, 65 (6): 1370- 1382 doi: 10.1109/TSP.2016.2634550
22	叶丽颖, 李静, 王金平. 具均匀衰减投影数据下发射型SPECT图像重建方法研究. 数学物理学报, 2018, 38A (3): 613- 624
	Ye L Y , Li J , Wang J P . Emission SPECT image reconstruction methods with uniformly attenuated projection data. Acta Math Sci, 2018, 38A (613): 624

Metrics

Viewed

Full text

268

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	4	0	0	264

	From	local

	Times	268
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	90

	From	Others

	Times	91
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

Comments

Recommended 10

[1]	Yang Xiangdong;Deng Guantie. Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1242 -1250 .
[2]	Liu Bingwen; Huang Lihong; Zhang Zhengqiu. Periodic Solutions for Nonlinear n-th Order Differential Equations with Delays[J]. Acta mathematica scientia,Series A, 2007, 27(2): 343 -350 .
[3]	Ding Jieli;Chen Xiru. Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear Models[J]. Acta mathematica scientia,Series A, 2006, 26(2): 168 -173 .
[4]	Zhang Wenzhuan;Tang Niansheng ; Wang Xueren. Confidence Regions in Nonlinear Reproductive Dispersion Mixed Models in Terms of Curvatures[J]. Acta mathematica scientia,Series A, 2006, 26(4): 547 -558 .
[5]	Zheng Shenzhou;Zhao Shule. Full Regularity of {\boldmath $p$ }-Harmonic Type Systems Below the Critical Growth [J]. Acta mathematica scientia,Series A, 2008, 28(3): 480 -488 .
[6]	SUN Dao-Chun. Random Meromorphic Functions in the Unit Disc[J]. Acta mathematica scientia,Series A, 2009, 29(3): 623 -629 .
[7]	ZHOU Zhen-Rong. Regularity of Subelliptic Q Harmonic Maps into Homogeneous Manifolds[J]. Acta mathematica scientia,Series A, 2005, 25(6): 799 -805 .
[8]	FANG Cong-Na, WANG Quan-Yi. The Existence and Uniqueness and Global Attraction of Periodic Solutions for a Class of Functional Differential Equations[J]. Acta mathematica scientia,Series A, 2005, 25(6): 913 -925 .
[9]	DU Ning. A Modified Upwind Difference Scheme and Convergence Analysis for Problem of Contamination by Compressible Nuclear Waste[J]. Acta mathematica scientia,Series A, 2005, 25(7): 1046 -1054 .
[10]	ZHANG Zi-Zhen, ZHANG Li-Chun,ZHAO Ren. Entropy of Cylindrical Black Hole[J]. Acta mathematica scientia,Series A, 2005, 25(7): 1061 -1066 .

SNR	支撑的识别
337.85	成功
187.69	成功
112.62	成功
93.85	成功
80.44	成功
3.38	失败

Exact Support Recovery of Sparse Signals from Noisy Measurements

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 6

References 22

Related Articles 1

Metrics

Comments

Recommended 10