# American Institute of Mathematical Sciences

• Previous Article
On the missing bound state data of inverse spectral-scattering problems on the half-line
• IPI Home
• This Issue
• Next Article
Estimation of conductivity changes in a region of interest with electrical impedance tomography
February  2015, 9(1): 231-238. doi: 10.3934/ipi.2015.9.231

## Sparse signals recovery from noisy measurements by orthogonal matching pursuit

 1 Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China 2 Department of Mathematics, Zhejiang University, Hangzhou, 310027

Received  June 2011 Revised  July 2013 Published  January 2015

Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to analysis OMP. We show that, under certain conditions based on the restricted isometry property and the signals, OMP will recover the support of the sparse signal when measurements are corrupted by additive noise.
Citation: Yi Shen, Song Li. Sparse signals recovery from noisy measurements by orthogonal matching pursuit. Inverse Problems & Imaging, 2015, 9 (1) : 231-238. doi: 10.3934/ipi.2015.9.231
##### References:

show all references

##### References:
 [1] Ying Zhang, Ling Ma, Zheng-Hai Huang. On phaseless compressed sensing with partially known support. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1519-1526. doi: 10.3934/jimo.2019014 [2] Steven L. Brunton, Joshua L. Proctor, Jonathan H. Tu, J. Nathan Kutz. Compressed sensing and dynamic mode decomposition. Journal of Computational Dynamics, 2015, 2 (2) : 165-191. doi: 10.3934/jcd.2015002 [3] Amin Boumenir, Vu Kim Tuan. Recovery of the heat coefficient by two measurements. Inverse Problems & Imaging, 2011, 5 (4) : 775-791. doi: 10.3934/ipi.2011.5.775 [4] Amin Boumenir, Vu Kim Tuan, Nguyen Hoang. The recovery of a parabolic equation from measurements at a single point. Evolution Equations & Control Theory, 2018, 7 (2) : 197-216. doi: 10.3934/eect.2018010 [5] Björn Popilka, Simon Setzer, Gabriele Steidl. Signal recovery from incomplete measurements in the presence of outliers. Inverse Problems & Imaging, 2007, 1 (4) : 661-672. doi: 10.3934/ipi.2007.1.661 [6] Yingying Li, Stanley Osher. Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm. Inverse Problems & Imaging, 2009, 3 (3) : 487-503. doi: 10.3934/ipi.2009.3.487 [7] Song Li, Junhong Lin. Compressed sensing with coherent tight frames via $l_q$-minimization for $0 < q \leq 1$. Inverse Problems & Imaging, 2014, 8 (3) : 761-777. doi: 10.3934/ipi.2014.8.761 [8] Anna-Lena Trautmann. Isometry and automorphisms of constant dimension codes. Advances in Mathematics of Communications, 2013, 7 (2) : 147-160. doi: 10.3934/amc.2013.7.147 [9] John A. Morgan. Interception in differential pursuit/evasion games. Journal of Dynamics & Games, 2016, 3 (4) : 335-354. doi: 10.3934/jdg.2016018 [10] Miroslava Růžičková, Irada Dzhalladova, Jitka Laitochová, Josef Diblík. Solution to a stochastic pursuit model using moment equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 473-485. doi: 10.3934/dcdsb.2018032 [11] Yangyang Xu, Wotao Yin, Stanley Osher. Learning circulant sensing kernels. Inverse Problems & Imaging, 2014, 8 (3) : 901-923. doi: 10.3934/ipi.2014.8.901 [12] Vikram Krishnamurthy, William Hoiles. Information diffusion in social sensing. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 365-411. doi: 10.3934/naco.2016017 [13] Thomas Feulner. The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes. Advances in Mathematics of Communications, 2009, 3 (4) : 363-383. doi: 10.3934/amc.2009.3.363 [14] Mohar Guha, Keith Promislow. Front propagation in a noisy, nonsmooth, excitable medium. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 617-638. doi: 10.3934/dcds.2009.23.617 [15] Alfred K. Louis. Diffusion reconstruction from very noisy tomographic data. Inverse Problems & Imaging, 2010, 4 (4) : 675-683. doi: 10.3934/ipi.2010.4.675 [16] Elena Braverman, Alexandra Rodkina. Stabilization of difference equations with noisy proportional feedback control. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2067-2088. doi: 10.3934/dcdsb.2017085 [17] Dana Paquin, Doron Levy, Lei Xing. Multiscale deformable registration of noisy medical images. Mathematical Biosciences & Engineering, 2008, 5 (1) : 125-144. doi: 10.3934/mbe.2008.5.125 [18] Jianzhong Wang. Wavelet approach to numerical differentiation of noisy functions. Communications on Pure & Applied Analysis, 2007, 6 (3) : 873-897. doi: 10.3934/cpaa.2007.6.873 [19] Peter Giesl, Boumediene Hamzi, Martin Rasmussen, Kevin Webster. Approximation of Lyapunov functions from noisy data. Journal of Computational Dynamics, 2019, 0 (0) : 0-0. doi: 10.3934/jcd.2020003 [20] Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42.

2018 Impact Factor: 1.469