-
Previous Article
A note on analyticity properties of far field patterns
- IPI Home
- This Issue
-
Next Article
Far field model for time reversal and application to selective focusing on small dielectric inhomogeneities
Source identification from line integral measurements and simple atmospheric models
1. | Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109-1043, United States |
2. | Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2370, United States |
3. | Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109 |
References:
[1] |
V. Akçelik, G. Biros, A. Draganeascu, J. Hill, O. Ghattas and B. van Bloemen Waanders, Dynamic data-driven inversion for terascale simulations: Real-time identification of airborne contaminants, in "Proceedings of the 2005 ACM/IEEE conference on Supercomputing," IEEE Computer Society, (2005), 43-57.
doi: 10.1109/SC.2005.25. |
[2] |
V. Akçelik, G. Biros, O. Ghattas, K. R. Long and B. van Bloemen Waanders, A variational finite element method for source inversion for convective-diffusive transport, Finite Elem. Anal. Des., 39 (2003), 683-705.
doi: 10.1016/S0168-874X(03)00054-4. |
[3] |
A. El Badia and T. Ha Duong, Some remarks on the problem of source identification from boundary measurements, Inverse Problems, 14 (1998), 883-891.
doi: 10.1088/0266-5611/14/4/008. |
[4] |
A. El Badia, T. Ha Duong and A. Hamdi, Identification of a point source in a linear advection-dispersion-reaction equation: Application to a pollution source problem, Inverse Problems, 21 (2005), 1121-1136.
doi: 10.1088/0266-5611/21/3/020. |
[5] |
A. Blake and A. Zisserman, "Visual Reconstruction," MIT Press, Cambridge, MA, 1987. |
[6] |
M. Burger, Y. Landa, N. M. Tanushev and R. Tsai, Discovering a point source in unknown environments, in "Algorithmic Foundation of Robotics VII" (eds. G. S. Chirikjian, H. Choset, M. Morales and T. Murphy), Springer, (2009), 663-678.
doi: 10.1007/978-3-642-00312-7_41. |
[7] |
E. J. Candes and T. Tao, Decoding by linear programming, IEEE Trans. Inform. Theory, 51 (2005), 4203-4215.
doi: 10.1109/TIT.2005.858979. |
[8] |
T. F. Chan and H.-M. Zhou, Total variation wavelet thresholding, J. Sci. Comput., 32 (2007), 315-341.
doi: 10.1007/s10915-007-9133-0. |
[9] |
R. Chartrand, Exact reconstruction of sparse signals via nonconvex minimization, Signal Processing Letters, 14 (2007), 707-710.
doi: 10.1109/LSP.2007.898300. |
[10] |
R. Chartrand and V. Staneva, Restricted isometry properties and nonconvex compressive sensing, Inverse Problems, 24 (2008).
doi: 10.1088/0266-5611/24/3/035020. |
[11] |
B. R. Cosofret, C. M. Gittins and W. J. Marinelli, Visualization and tomographic analysis of chemical vapor plumes via LWIR imaging Fabry-Perot spectrometry, in "Proc. SPIE: Chemical and Biological Standoff Detection II" (eds. J. O. Jensen and J.-M. Theriault), SPIE, (2004), 112-121.
doi: 10.1117/12.570442. |
[12] |
D. L. Donoho, Sparse components of images and optimal atomic decompositions, Constructive Approximation, 17 (2001), 353-382.
doi: 10.1007/s003650010032. |
[13] |
C. M. Gittins and W. J. Marinelli, AIRIS multispectral imaging chemical sensor, in "Proc. SPIE: Electro-Optical Technology for Remote Chemical Detection and Identification III" (eds. M. Fallahi and E. A. Howden), SPIE, (1998), 65-74.
doi: 10.1117/12.317637. |
[14] |
E. T. Hale, W. Yin and Y. Zhang, Fixed-point continuation for $l_1$-minimization: Methodology and convergence, SIAM J. Optim., 19 (2008), 1107-1130.
doi: 10.1137/070698920. |
[15] |
J. P. Kernévez, "The Sentinel Method and Its Application to Environmental Pollution Problems," CRC Press, New York, 1997. |
[16] |
Y. Landa, H. Shen, R. Takei and Y.-H. R. Tsai, Autonomous source discovery and navigation in complicated environments, UCLA CAM Report, (2009), 09-73. |
[17] |
Y. Li, S. Osher and R. Tsai, Heat source identification based on $L_1$ constrained minimization, UCLA CAM Report, (2011), 11-04. |
[18] |
L. Ling, M. Yamamoto, Y. C. Hon and T. Takeuchi, Identification of source locations in two-dimensional heat equations, Inverse Problems, 22 (2006), 1289-1305.
doi: 10.1088/0266-5611/22/4/011. |
[19] |
J. L. Lions, Pointwise control for distributed systems, in "Control and Estimation in Distributed Parameters Systems" (ed. H. T. Banks), SIAM, (1992), 1-39.
doi: 10.1137/1.9781611970982.ch1. |
[20] |
J. Rauch, "Partial Differential Equations," Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4612-0953-9. |
show all references
References:
[1] |
V. Akçelik, G. Biros, A. Draganeascu, J. Hill, O. Ghattas and B. van Bloemen Waanders, Dynamic data-driven inversion for terascale simulations: Real-time identification of airborne contaminants, in "Proceedings of the 2005 ACM/IEEE conference on Supercomputing," IEEE Computer Society, (2005), 43-57.
doi: 10.1109/SC.2005.25. |
[2] |
V. Akçelik, G. Biros, O. Ghattas, K. R. Long and B. van Bloemen Waanders, A variational finite element method for source inversion for convective-diffusive transport, Finite Elem. Anal. Des., 39 (2003), 683-705.
doi: 10.1016/S0168-874X(03)00054-4. |
[3] |
A. El Badia and T. Ha Duong, Some remarks on the problem of source identification from boundary measurements, Inverse Problems, 14 (1998), 883-891.
doi: 10.1088/0266-5611/14/4/008. |
[4] |
A. El Badia, T. Ha Duong and A. Hamdi, Identification of a point source in a linear advection-dispersion-reaction equation: Application to a pollution source problem, Inverse Problems, 21 (2005), 1121-1136.
doi: 10.1088/0266-5611/21/3/020. |
[5] |
A. Blake and A. Zisserman, "Visual Reconstruction," MIT Press, Cambridge, MA, 1987. |
[6] |
M. Burger, Y. Landa, N. M. Tanushev and R. Tsai, Discovering a point source in unknown environments, in "Algorithmic Foundation of Robotics VII" (eds. G. S. Chirikjian, H. Choset, M. Morales and T. Murphy), Springer, (2009), 663-678.
doi: 10.1007/978-3-642-00312-7_41. |
[7] |
E. J. Candes and T. Tao, Decoding by linear programming, IEEE Trans. Inform. Theory, 51 (2005), 4203-4215.
doi: 10.1109/TIT.2005.858979. |
[8] |
T. F. Chan and H.-M. Zhou, Total variation wavelet thresholding, J. Sci. Comput., 32 (2007), 315-341.
doi: 10.1007/s10915-007-9133-0. |
[9] |
R. Chartrand, Exact reconstruction of sparse signals via nonconvex minimization, Signal Processing Letters, 14 (2007), 707-710.
doi: 10.1109/LSP.2007.898300. |
[10] |
R. Chartrand and V. Staneva, Restricted isometry properties and nonconvex compressive sensing, Inverse Problems, 24 (2008).
doi: 10.1088/0266-5611/24/3/035020. |
[11] |
B. R. Cosofret, C. M. Gittins and W. J. Marinelli, Visualization and tomographic analysis of chemical vapor plumes via LWIR imaging Fabry-Perot spectrometry, in "Proc. SPIE: Chemical and Biological Standoff Detection II" (eds. J. O. Jensen and J.-M. Theriault), SPIE, (2004), 112-121.
doi: 10.1117/12.570442. |
[12] |
D. L. Donoho, Sparse components of images and optimal atomic decompositions, Constructive Approximation, 17 (2001), 353-382.
doi: 10.1007/s003650010032. |
[13] |
C. M. Gittins and W. J. Marinelli, AIRIS multispectral imaging chemical sensor, in "Proc. SPIE: Electro-Optical Technology for Remote Chemical Detection and Identification III" (eds. M. Fallahi and E. A. Howden), SPIE, (1998), 65-74.
doi: 10.1117/12.317637. |
[14] |
E. T. Hale, W. Yin and Y. Zhang, Fixed-point continuation for $l_1$-minimization: Methodology and convergence, SIAM J. Optim., 19 (2008), 1107-1130.
doi: 10.1137/070698920. |
[15] |
J. P. Kernévez, "The Sentinel Method and Its Application to Environmental Pollution Problems," CRC Press, New York, 1997. |
[16] |
Y. Landa, H. Shen, R. Takei and Y.-H. R. Tsai, Autonomous source discovery and navigation in complicated environments, UCLA CAM Report, (2009), 09-73. |
[17] |
Y. Li, S. Osher and R. Tsai, Heat source identification based on $L_1$ constrained minimization, UCLA CAM Report, (2011), 11-04. |
[18] |
L. Ling, M. Yamamoto, Y. C. Hon and T. Takeuchi, Identification of source locations in two-dimensional heat equations, Inverse Problems, 22 (2006), 1289-1305.
doi: 10.1088/0266-5611/22/4/011. |
[19] |
J. L. Lions, Pointwise control for distributed systems, in "Control and Estimation in Distributed Parameters Systems" (ed. H. T. Banks), SIAM, (1992), 1-39.
doi: 10.1137/1.9781611970982.ch1. |
[20] |
J. Rauch, "Partial Differential Equations," Springer-Verlag, New York, 1991.
doi: 10.1007/978-1-4612-0953-9. |
[1] |
Qing Tang. On an optimal control problem of time-fractional advection-diffusion equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (2) : 761-779. doi: 10.3934/dcdsb.2019266 |
[2] |
Assyr Abdulle. Multiscale methods for advection-diffusion problems. Conference Publications, 2005, 2005 (Special) : 11-21. doi: 10.3934/proc.2005.2005.11 |
[3] |
Lena-Susanne Hartmann, Ilya Pavlyukevich. Advection-diffusion equation on a half-line with boundary Lévy noise. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 637-655. doi: 10.3934/dcdsb.2018200 |
[4] |
S. Sadeghi, H. Jafari, S. Nemati. Solving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3747-3761. doi: 10.3934/dcdss.2020435 |
[5] |
Michael Taylor. Random walks, random flows, and enhanced diffusivity in advection-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1261-1287. doi: 10.3934/dcdsb.2012.17.1261 |
[6] |
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 |
[7] |
Ying Zhang, Ling Ma, Zheng-Hai Huang. On phaseless compressed sensing with partially known support. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1519-1526. doi: 10.3934/jimo.2019014 |
[8] |
Alexandre Caboussat, Roland Glowinski. A Numerical Method for a Non-Smooth Advection-Diffusion Problem Arising in Sand Mechanics. Communications on Pure and Applied Analysis, 2009, 8 (1) : 161-178. doi: 10.3934/cpaa.2009.8.161 |
[9] |
Patrick Henning, Mario Ohlberger. The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift. Networks and Heterogeneous Media, 2010, 5 (4) : 711-744. doi: 10.3934/nhm.2010.5.711 |
[10] |
Patrick Henning, Mario Ohlberger. A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1393-1420. doi: 10.3934/dcdss.2016056 |
[11] |
Masahiro Yamamoto. Uniqueness for inverse problem of determining fractional orders for time-fractional advection-diffusion equations. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022017 |
[12] |
Zohre Aminifard, Saman Babaie-Kafaki. Diagonally scaled memoryless quasi–Newton methods with application to compressed sensing. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021191 |
[13] |
Shousheng Luo, Tie Zhou. Superiorization of EM algorithm and its application in Single-Photon Emission Computed Tomography(SPECT). Inverse Problems and Imaging, 2014, 8 (1) : 223-246. doi: 10.3934/ipi.2014.8.223 |
[14] |
Vikram Krishnamurthy, William Hoiles. Information diffusion in social sensing. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 365-411. doi: 10.3934/naco.2016017 |
[15] |
Yingying Li, Stanley Osher. Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm. Inverse Problems and Imaging, 2009, 3 (3) : 487-503. doi: 10.3934/ipi.2009.3.487 |
[16] |
Song Li, Junhong Lin. Compressed sensing with coherent tight frames via $l_q$-minimization for $0 < q \leq 1$. Inverse Problems and Imaging, 2014, 8 (3) : 761-777. doi: 10.3934/ipi.2014.8.761 |
[17] |
Henrik Garde, Kim Knudsen. 3D reconstruction for partial data electrical impedance tomography using a sparsity prior. Conference Publications, 2015, 2015 (special) : 495-504. doi: 10.3934/proc.2015.0495 |
[18] |
Linfei Wang, Dapeng Tao, Ruonan Wang, Ruxin Wang, Hao Li. Big Map R-CNN for object detection in large-scale remote sensing images. Mathematical Foundations of Computing, 2019, 2 (4) : 299-314. doi: 10.3934/mfc.2019019 |
[19] |
Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reaction-diffusion patterns. Communications on Pure and Applied Analysis, 2012, 11 (1) : 189-207. doi: 10.3934/cpaa.2012.11.189 |
[20] |
Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reaction-diffusion equations. Kinetic and Related Models, 2010, 3 (3) : 427-444. doi: 10.3934/krm.2010.3.427 |
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]