Year: 2015
Author: Zhiqiang Xu
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 495–516
Abstract
The orthogonal multi-matching pursuit (OMMP) is a natural extension of the orthogonal matching pursuit (OMP).We denote the OMMP with the parameter $M$ as OMMP($M$) where $M$ ≥ 1 is an integer. The main difference between OMP and OMMP($M$) is that OMMP($M$) selects $M$ atoms per iteration, while OMP only adds one atom to the optimal atom set. In this paper, we study the performance of orthogonal multi-matching pursuit under RIP. In particular, we show that, when the measurement matrix $A$ satisfies (25$s$, 1/10)-RIP, OMMP($M_0$) with $M_0$ = 12 can recover $s$-sparse signals within $s$ iterations. We furthermore prove that OMMP($M$) can recover $s$-sparse signals within $O(s/M)$ iterations for a large class of $M$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1505-m4529
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 495–516
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Sparse signals Compressed sensing Greedy algorithms
Author Details
-
From theoretical guarantee to practical performance: selectable and optimal step-lengths for IHT and HTP algorithms in compressed sensing
Xie, Lie-Jun | Jin, WenComputational and Applied Mathematics, Vol. 44 (2025), Iss. 1
https://doi.org/10.1007/s40314-024-02962-6 [Citations: 0] -
Restricted isometry constant improvement based on a singular value decomposition‐weighted measurement matrix for compressed sensing
Wang, Qian | Qu, GangrongIET Communications, Vol. 11 (2017), Iss. 11 P.1706
https://doi.org/10.1049/iet-com.2016.1435 [Citations: 8] -
A 232–1996-kS/s Robust Compressive Sensing Reconstruction Engine for Real-Time Physiological Signals Monitoring
Chen, Ting-Sheng | Kuo, Hung-Chi | Wu, An-YeuIEEE Journal of Solid-State Circuits, Vol. 54 (2019), Iss. 1 P.307
https://doi.org/10.1109/JSSC.2018.2869887 [Citations: 15] -
Greedy algorithms for sparse signal recovery based on temporally correlated experimental data in WSNs
Goyal, Poonam | Singh, BrahmjitArabian Journal for Science and Engineering, Vol. 43 (2018), Iss. 12 P.7253
https://doi.org/10.1007/s13369-017-3001-5 [Citations: 1] -
Sharp sufficient conditions for stable recovery of block sparse signals by block orthogonal matching pursuit
Wen, Jinming | Zhou, Zhengchun | Liu, Zilong | Lai, Ming-Jun | Tang, XiaohuApplied and Computational Harmonic Analysis, Vol. 47 (2019), Iss. 3 P.948
https://doi.org/10.1016/j.acha.2018.02.002 [Citations: 43] -
A Signal Dependent Analysis of Orthogonal Least Squares Based on the Restricted Isometry Property
Bosse, Jonathan
IEEE Transactions on Signal Processing, Vol. 71 (2023), Iss. P.1574
https://doi.org/10.1109/TSP.2023.3267009 [Citations: 0] -
Nearly optimal number of iterations for sparse signal recovery with orthogonal multi-matching pursuit *
Li, Haifeng | Wen, Jinming | Xian, Jun | Zhang, JingInverse Problems, Vol. 37 (2021), Iss. 11 P.115007
https://doi.org/10.1088/1361-6420/ac2cdd [Citations: 1] -
A sharp recovery condition for block sparse signals by block orthogonal multi-matching pursuit
Chen, WenGu | Ge, HuanMinScience China Mathematics, Vol. 60 (2017), Iss. 7 P.1325
https://doi.org/10.1007/s11425-016-0448-7 [Citations: 7] -
Optimization Methods of Compressively Sensed Image Reconstruction Based on Single-Pixel Imaging
Wei, Ziran | Zhang, Jianlin | Xu, Zhiyong | Liu, YongApplied Sciences, Vol. 10 (2020), Iss. 9 P.3288
https://doi.org/10.3390/app10093288 [Citations: 10] -
Sparse Signal Recovery Through Regularized Orthogonal Matching Pursuit for WSNs Applications
Goyal, Poonam | Singh, Brahmjit2019 6th International Conference on Signal Processing and Integrated Networks (SPIN), (2019), P.461
https://doi.org/10.1109/SPIN.2019.8711716 [Citations: 4] -
One-Bit Compressed Sensing by Greedy Algorithms
Liu, Wenhui | Gong, Da | Xu, ZhiqiangNumerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 2 P.169
https://doi.org/10.4208/nmtma.2016.m1428 [Citations: 8] -
Structured Measurement Matrices Based on Deterministic Fourier Matrices and Gram Matrices
Zhang, Guojun | Gao, YiCircuits, Systems, and Signal Processing, Vol. 43 (2024), Iss. 8 P.5121
https://doi.org/10.1007/s00034-024-02692-4 [Citations: 0] -
Binary generalized orthogonal matching pursuit
Li, Haifeng | Ying, Hao | Liu, XiaoliJapan Journal of Industrial and Applied Mathematics, Vol. 41 (2024), Iss. 1 P.1
https://doi.org/10.1007/s13160-023-00585-8 [Citations: 1] -
Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery
Shao, Chunfang | Wei, Xiujie | Ye, Peixin | Xing, ShuoAxioms, Vol. 12 (2023), Iss. 4 P.389
https://doi.org/10.3390/axioms12040389 [Citations: 2] -
Improved bounds for the RIP of Subsampled Circulant Matrices
Huang, Meng | Pang, Yuxuan | Xu, ZhiqiangSampling Theory in Signal and Image Processing, Vol. 18 (2019), Iss. 1 P.1
https://doi.org/10.1007/BF03549617 [Citations: 0] -
Wavelet Decomposition optimization via Exponential Decay Constraint for Compressively Sensed Image Reconstruction
Wei, Ziran | Zhang, Jianlin | Xu, Zhiyong | Liu, Yong2020 International Conference on Computer Vision, Image and Deep Learning (CVIDL), (2020), P.160
https://doi.org/10.1109/CVIDL51233.2020.00038 [Citations: 0] -
Measurement Matrix Optimization via Mutual Coherence Minimization for Compressively Sensed Signals Reconstruction
Wei, Ziran | Zhang, Jianlin | Xu, Zhiyong | Liu, Yong | Okarma, KrzysztofMathematical Problems in Engineering, Vol. 2020 (2020), Iss. P.1
https://doi.org/10.1155/2020/7979606 [Citations: 10]