基于OMMP算法的多测量向量问题的重构
PDF下载 (169)冯晓艳,王金平.基于OMMP算法的多测量向量问题的重构[J].宁波大学学报(理工版),2024,37(1):43-50.DOI:10.20098/j.cnki.1001-5132.2023.0320
FENG Xiaoyan,WANG Jinping.Reconstruction of MMV problem based on OMMP algorithm[J].Journal of Ningbo University(Natural Science & Engineering Edition),2024,37(1):43-50.DOI:10.20098/j.cnki.1001-5132.2023.0320
| Title: | Reconstruction of MMV problem based on OMMP algorithm |
| 作者: | 冯晓艳, 王金平 |
| Author(s): | FENG Xiaoyan, WANG Jinping |
| 关键词: | 压缩感知; 正交多匹配追踪; 限制等距性; 多测量向量 |
| Keywords: | compressed sensing; orthogonal multi-matching pursuit; restricted isometry property; multiple measurement vector |
| 分类号: | O177.92; O29 |
| DOI: | 10.20098/j.cnki.1001-5132.2023.0320 |
| 文献标识码: | A |
| 摘要: | 正交多匹配追踪算法(OMMP算法)是正交匹配追踪算法(OMP算法)的一种拓展, 近年来受到很多相关研究人员的关注. 不同于OMP算法, OMMP算法在每次迭代中识别多个指标. 本文分析了在限制等距性(RIP)和多向量信噪比(MSNR)条件下, 用于解决多测量向量问题的OMMP算法的鲁棒性. 此外, 在给出的限制等距常数(RIC)的条件下, 用归纳假设的方法证明了当V=0以及整数 满足1≤N≤(m-1)/K时, OMMP算法可以准确恢复K-行稀疏矩阵X. |
| Abstract: | As an extension of OMP, orthogonal multi-matching pursuit (OMMP) has received much attention in recent years. Unlike the OMP, OMMP algorithm identifies N≥1 indexes per iteration. In this paper, the robustness of the OMMP for multiple measurement vector (MMV) problem under the restricted isometry property (RIP) and multi-signal-to-noise ratio (MSNR), which will be mentioned in introduction, is presented. Furthermore, the induction hypothesis is used to show that the OMMP algorithm can exactly recover K-row sparse matrix in K iterations under the RIP condition presented when V=0 and integer with 1≤N≤(m-1)/K. |
| 参考文献 /References: | [1] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306. [2] CANDES E J, TAO T. Decoding by linear programming[J]. IEEE Transactions on Information Theory, 2005, 51(12):4203-4215. [3] WAKIN M B, LASKA J N, DUARTE M F, et al. An architecture for compressive imaging[C]//2006 International Conference on Image Processing. Atlanta, GA, USA. IEEE, 2006:1273-1276. [4] DONOHO D L, ELAD M, TEMLYAKOV V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE Transactions on Information Theory, 2006, 52(1):6-18. [5] HERMAN M A, STROHMER T. High-resolution radar via compressed sensing[J]. IEEE Transactions on Signal Processing, 2009, 57(6):2275-2284. [6] LUSTIG M, DONOHO D L, SANTOS J M, et al. Compressed sensing MRI[J]. IEEE Signal Processing Magazine, 2008, 25(2):72-82. [7] CHEN J, HUO X M. Theoretical results on sparse representations of multiple-measurement vectors[J]. IEEE Transactions on Signal Processing, 2006, 54(12):4634-4643. [8] WANG Y, FU T, GAO M G, et al. Performance of orthogonal matching pursuit for multiple measurement vectors with noise[C]//2013 IEEE China Summit and International Conference on Signal and Information Processing. Beijing, China, 2013:67-71. [9] LI H F, WANG L B, ZHAN X Q, et al. On the fundamental limit of orthogonal matching pursuit for multiple measurement vector[J]. IEEE Access, 2019, 7:48860-48866. [10] COTTER S F, RAO B D, ENGAN K, et al. Sparse solutions to linear inverse problems with multiple measurement vectors[J]. IEEE Transactions on Signal Processing, 2005, 53(7):2477-2488. [11] MALIOUTOV D, CETIN M, WILLSKY A S. A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Transactions on Signal Processing, 2005, 53(8):3010-3022. [12] WEN J M, LI D F, ZHU F M. Stable recovery of sparse signals via lp-minimization[J]. Applied and Computational Harmonic Analysis, 2015, 38(1):161-176. [13] 卜京, 王金平. 混合最小化问题下重构块稀疏信号的充分条件[J]. 武汉大学学报(理学版), 2021, 67(2):185-189. [14] LIU E T, TEMLYAKOV V N. The orthogonal super greedy algorithm and applications in compressed sensing[J]. IEEE Transactions on Information Theory, 2012, 58(4):2040-2047. [15] WANG J, KWON S, SHIM B. Generalized orthogonal matching pursuit[J]. IEEE Transactions on Signal Processing, 2012, 60(12):6202-6216. [16] SATPATHI S, DAS R L, CHAKRABORTY M. Improving the bound on the RIP constant in generalized orthogonal matching pursuit[J]. IEEE Signal Processing Letters, 2013, 20(11):1074-1077. [17] SHEN Y, LI B, PAN W L, et al. Analysis of generalised orthogonal matching pursuit using restricted isometry constant[J]. Electronics Letters, 2014, 50(14):1020-1022. [18] WEN J M, ZHOU Z C, LI D F, et al. A novel sufficient condition for generalized orthogonal matching pursuit[J]. IEEE Communications Letters, 2017, 21(4):805-808. [19] WANG J. Support recovery with orthogonal matching pursuit in the presence of noise[J]. IEEE Transactions on Signal Processing, 2015, 63(21):5868-5877. [20] NEEDELL D, TROPP J A. CoSaMP: iterative signal recovery from incomplete and inaccurate samples[J]. Applied and Computational Harmonic Analysis, 2009, 26(3):301-321. [21] WEN J M, TANG J, ZHU F M. Greedy block coordinate descent under restricted isometry property[J]. Mobile Networks and Applications, 2017, 22(3):371-376. [22] ZHANG X W, XIE L J, WANG J P. Some results on OMP algorithm for MMV problem[J]. Mathematical Methods in the Applied Sciences, 2022, 45(9):5402-5411. [23] WEN J M, ZHOU Z C, WANG J, et al. A sharp condition for exact support recovery with orthogonal matching pursuit[J]. IEEE Transactions on Signal Processing, 2017, 65(6):1370-1382. |
| 备注/Memo: | 收稿日期: 2023－03－17. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（62071262）. 第一作者: 冯晓艳, 硕士研究生, 主要研究方向: 积分变换与图像处理. E-mail: 2933667080@qq.com *通信作者: 王金平, 博士/教授, 主要研究方向: 积分变换与图像处理. E-mail: wangjinping@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
