June  2014, 19(4): 979-998. doi: 10.3934/dcdsb.2014.19.979

High frequency analysis of imaging with noise blending

1. 

Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Received  October 2012 Revised  January 2014 Published  April 2014

We consider sensor array imaging for simultaneous noise blended sources. We study a migration imaging functional and we analyze its sensitivity to singular perturbations of the speed of propagation of the medium. We consider two kinds of random sources: randomly delayed pulses and stationary random processes, and three possible kinds of perturbations. Using high frequency analysis we prove the statistical stability (with respect to the realization of the noise blending) of the scheme and obtain quantitative results on the image contrast provided by the imaging functional, which strongly depends on the type of perturbations.
Citation: Ennio Fedrizzi. High frequency analysis of imaging with noise blending. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 979-998. doi: 10.3934/dcdsb.2014.19.979
References:
[1]

Inverse Problems, 24 (2008), 015011. doi: 10.1088/0266-5611/24/1/015011.  Google Scholar

[2]

The Leading Edge, 27 (2008), 924-938. doi: 10.1190/1.2954035.  Google Scholar

[3]

Springer-Verlag, New York, 2001.  Google Scholar

[4]

Nature Geoscience, 1 (2008), 126-130. doi: 10.1038/ngeo104.  Google Scholar

[5]

Geophysical Research Letters, 34 (2007), L02305. doi: 10.1029/2006GL028586.  Google Scholar

[6]

The Leading Edge, 25 (2006), 1082-1092. doi: 10.1190/1.2349814.  Google Scholar

[7]

Contemporary Mathematics, 577 (2012), 105-124. doi: 10.1090/conm/577/11466.  Google Scholar

[8]

Reports on Progress in Physics, 63 (2000), 1933-1995. doi: 10.1088/0034-4885/63/12/202.  Google Scholar

[9]

Springer, New York, 2007.  Google Scholar

[10]

SIAM Journal on Imaging Sciences, 2 (2009), 396-437. doi: 10.1137/080723454.  Google Scholar

[11]

Inverse Problems, 26 (2010), 074001. doi: 10.1088/0266-5611/26/7/074001.  Google Scholar

[12]

Geophysical Prospecting, 56 (2008), 375-393. doi: 10.1111/j.1365-2478.2007.00684.x.  Google Scholar

[13]

The Leading Edge, 27 (2008), 918-923. doi: 10.1190/1.2954034.  Google Scholar

[14]

Geophysics, 71 (2006), SI11-SI21. doi: 10.1190/1.2213356.  Google Scholar

[15]

Geophysics, 76 (2011), Q9-Q17. doi: 10.1190/1.3556597.  Google Scholar

[16]

Geophysical Research Letters, 33 (2006), L06313. doi: 10.1029/2005GL025563.  Google Scholar

[17]

Geophysical Journal International, 184 (2011), 1289-1303. doi: 10.1111/j.1365-246X.2010.04906.x.  Google Scholar

[18]

Science, 307 (2005), 1615-1618. doi: 10.1126/science.1108339.  Google Scholar

[19]

Journal of Geophysical Research, 111 (2006), B10306. doi: 10.1029/2005JB004237.  Google Scholar

[20]

Geophysics, 76 (2011), A7-A13. doi: 10.1190/1.3521658.  Google Scholar

[21]

Geophysical Prospecting, 60 (2012), 802-823. doi: 10.1111/j.1365-2478.2012.01056.x.  Google Scholar

show all references

References:
[1]

Inverse Problems, 24 (2008), 015011. doi: 10.1088/0266-5611/24/1/015011.  Google Scholar

[2]

The Leading Edge, 27 (2008), 924-938. doi: 10.1190/1.2954035.  Google Scholar

[3]

Springer-Verlag, New York, 2001.  Google Scholar

[4]

Nature Geoscience, 1 (2008), 126-130. doi: 10.1038/ngeo104.  Google Scholar

[5]

Geophysical Research Letters, 34 (2007), L02305. doi: 10.1029/2006GL028586.  Google Scholar

[6]

The Leading Edge, 25 (2006), 1082-1092. doi: 10.1190/1.2349814.  Google Scholar

[7]

Contemporary Mathematics, 577 (2012), 105-124. doi: 10.1090/conm/577/11466.  Google Scholar

[8]

Reports on Progress in Physics, 63 (2000), 1933-1995. doi: 10.1088/0034-4885/63/12/202.  Google Scholar

[9]

Springer, New York, 2007.  Google Scholar

[10]

SIAM Journal on Imaging Sciences, 2 (2009), 396-437. doi: 10.1137/080723454.  Google Scholar

[11]

Inverse Problems, 26 (2010), 074001. doi: 10.1088/0266-5611/26/7/074001.  Google Scholar

[12]

Geophysical Prospecting, 56 (2008), 375-393. doi: 10.1111/j.1365-2478.2007.00684.x.  Google Scholar

[13]

The Leading Edge, 27 (2008), 918-923. doi: 10.1190/1.2954034.  Google Scholar

[14]

Geophysics, 71 (2006), SI11-SI21. doi: 10.1190/1.2213356.  Google Scholar

[15]

Geophysics, 76 (2011), Q9-Q17. doi: 10.1190/1.3556597.  Google Scholar

[16]

Geophysical Research Letters, 33 (2006), L06313. doi: 10.1029/2005GL025563.  Google Scholar

[17]

Geophysical Journal International, 184 (2011), 1289-1303. doi: 10.1111/j.1365-246X.2010.04906.x.  Google Scholar

[18]

Science, 307 (2005), 1615-1618. doi: 10.1126/science.1108339.  Google Scholar

[19]

Journal of Geophysical Research, 111 (2006), B10306. doi: 10.1029/2005JB004237.  Google Scholar

[20]

Geophysics, 76 (2011), A7-A13. doi: 10.1190/1.3521658.  Google Scholar

[21]

Geophysical Prospecting, 60 (2012), 802-823. doi: 10.1111/j.1365-2478.2012.01056.x.  Google Scholar

[1]

Deconinck Bernard, Olga Trichtchenko. High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1323-1358. doi: 10.3934/dcds.2017055

[2]

Jingzhi Li, Hongyu Liu, Hongpeng Sun, Jun Zou. Imaging acoustic obstacles by singular and hypersingular point sources. Inverse Problems & Imaging, 2013, 7 (2) : 545-563. doi: 10.3934/ipi.2013.7.545

[3]

Eduard Feireisl, Dalibor Pražák. A stabilizing effect of a high-frequency driving force on the motion of a viscous, compressible, and heat conducting fluid. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 95-111. doi: 10.3934/dcdss.2009.2.95

[4]

Josselin Garnier. Ghost imaging in the random paraxial regime. Inverse Problems & Imaging, 2016, 10 (2) : 409-432. doi: 10.3934/ipi.2016006

[5]

Xiaoping Fang, Youjun Deng, Wing-Yan Tsui, Zaiyun Zhang. On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements. Electronic Research Archive, 2020, 28 (3) : 1239-1255. doi: 10.3934/era.2020068

[6]

Christian Lax, Sebastian Walcher. Singular perturbations and scaling. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 1-29. doi: 10.3934/dcdsb.2019170

[7]

Peter W. Bates, Ji Li, Mingji Zhang. Singular fold with real noise. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2091-2107. doi: 10.3934/dcdsb.2016038

[8]

Li Shen, Eric Todd Quinto, Shiqiang Wang, Ming Jiang. Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography. Inverse Problems & Imaging, 2018, 12 (6) : 1343-1364. doi: 10.3934/ipi.2018056

[9]

Lan Qiao, Sining Zheng. Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1113-1129. doi: 10.3934/cpaa.2007.6.1113

[10]

Zvi Artstein. Invariance principle in the singular perturbations limit. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309

[11]

Fuke Wu, George Yin, Zhuo Jin. Kolmogorov-type systems with regime-switching jump diffusion perturbations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2293-2319. doi: 10.3934/dcdsb.2016048

[12]

Yuanjia Ma. The optimization algorithm for blind processing of high frequency signal of capacitive sensor. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1399-1412. doi: 10.3934/dcdss.2019096

[13]

Guillaume Bal. Homogenization in random media and effective medium theory for high frequency waves. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 473-492. doi: 10.3934/dcdsb.2007.8.473

[14]

François Genoud. Existence and stability of high frequency standing waves for a nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1229-1247. doi: 10.3934/dcds.2009.25.1229

[15]

Mathias Fink, Josselin Garnier. Ambient noise correlation-based imaging with moving sensors. Inverse Problems & Imaging, 2017, 11 (3) : 477-500. doi: 10.3934/ipi.2017022

[16]

Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567

[17]

Michel Chipot, Senoussi Guesmia. On the asymptotic behavior of elliptic, anisotropic singular perturbations problems. Communications on Pure & Applied Analysis, 2009, 8 (1) : 179-193. doi: 10.3934/cpaa.2009.8.179

[18]

Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363

[19]

Chiara Zanini. Singular perturbations of finite dimensional gradient flows. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 657-675. doi: 10.3934/dcds.2007.18.657

[20]

Canela Jordi. Singular perturbations of Blaschke products and connectivity of Fatou components. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 3567-3585. doi: 10.3934/dcds.2017153

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (34)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]