American Institute of Mathematical Sciences

Advanced
November  2009, 3(4): 711-730. doi: 10.3934/ipi.2009.3.711

Model reduction and pollution source identification from remote sensing data

A Voutilainen 1, and  Jari P. Kaipio 2,

1. 

Department of Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio
2. 

Department of Physics, University of Kuopio, P.O.Box 1627, 70211 Kuopio, Finland

Received  December 2008 Revised  July 2009 Published  October 2009

We consider a source identification problem related to determination of contaminant source parameters in lake environments using remote sensing measurements. We carry out a numerical example case study in which we employ the statistical inversion approach for the determination of the source parameters. In the simulation study a pipeline breaks on the bottom of a lake and only low-resolution remote sensing measurements are available. We also describe how model uncertainties and especially errors that are related to model reduction are taken into account in the overall statistical model of the system. The results indicate that the estimates may be heavily misleading if the statistics of the model errors are not taken into account.
Keywords: approximation error, Bayesian inference., model reduction, inverse problem, Source identification.
Mathematics Subject Classification: Primary: 35R30, 65N21; Secondary: 62F1.
Citation: A Voutilainen, Jari P. Kaipio. Model reduction and pollution source identification from remote sensing data. Inverse Problems & Imaging, 2009, 3 (4) : 711-730. doi: 10.3934/ipi.2009.3.711
[1]

Martin Hanke, William Rundell. On rational approximation methods for inverse source problems. Inverse Problems & Imaging, 2011, 5 (1) : 185-202. doi: 10.3934/ipi.2011.5.185
[2]

Evangelos Evangelou. Approximate Bayesian inference for geostatistical generalised linear models. Foundations of Data Science, 2019, 1 (1) : 39-60. doi: 10.3934/fods.2019002
[3]

Luciano Pandolfi. Riesz systems, spectral controllability and a source identification problem for heat equations with memory. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 745-759. doi: 10.3934/dcdss.2011.4.745
[4]

Pavel Krejčí. The Preisach hysteresis model: Error bounds for numerical identification and inversion. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 101-119. doi: 10.3934/dcdss.2013.6.101
[5]

Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417
[6]

Masoumeh Dashti, Stephen Harris, Andrew Stuart. Besov priors for Bayesian inverse problems. Inverse Problems & Imaging, 2012, 6 (2) : 183-200. doi: 10.3934/ipi.2012.6.183
[7]

Peijun Li, Ganghua Yuan. Increasing stability for the inverse source scattering problem with multi-frequencies. Inverse Problems & Imaging, 2017, 11 (4) : 745-759. doi: 10.3934/ipi.2017035
[8]

Kenichi Sakamoto, Masahiro Yamamoto. Inverse source problem with a final overdetermination for a fractional diffusion equation. Mathematical Control & Related Fields, 2011, 1 (4) : 509-518. doi: 10.3934/mcrf.2011.1.509
[9]

Shumin Li, Masahiro Yamamoto, Bernadette Miara. A Carleman estimate for the linear shallow shell equation and an inverse source problem. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 367-380. doi: 10.3934/dcds.2009.23.367
[10]

Yuxuan Gong, Xiang Xu. Inverse random source problem for biharmonic equation in two dimensions. Inverse Problems & Imaging, 2019, 13 (3) : 635-652. doi: 10.3934/ipi.2019029
[11]

Martin Redmann, Peter Benner. Approximation and model order reduction for second order systems with Levy-noise. Conference Publications, 2015, 2015 (special) : 945-953. doi: 10.3934/proc.2015.0945
[12]

Lili Chang, Wei Gong, Guiquan Sun, Ningning Yan. PDE-constrained optimal control approach for the approximation of an inverse Cauchy problem. Inverse Problems & Imaging, 2015, 9 (3) : 791-814. doi: 10.3934/ipi.2015.9.791
[13]

Guanghui Hu, Peijun Li, Xiaodong Liu, Yue Zhao. Inverse source problems in electrodynamics. Inverse Problems & Imaging, 2018, 12 (6) : 1411-1428. doi: 10.3934/ipi.2018059
[14]

Georg Vossen, Stefan Volkwein. Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 465-485. doi: 10.3934/naco.2012.2.465
[15]

Guillaume Bal, Ian Langmore, Youssef Marzouk. Bayesian inverse problems with Monte Carlo forward models. Inverse Problems & Imaging, 2013, 7 (1) : 81-105. doi: 10.3934/ipi.2013.7.81
[16]

Mila Nikolova. Model distortions in Bayesian MAP reconstruction. Inverse Problems & Imaging, 2007, 1 (2) : 399-422. doi: 10.3934/ipi.2007.1.399
[17]

Atsushi Kawamoto. Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation. Inverse Problems & Imaging, 2018, 12 (2) : 315-330. doi: 10.3934/ipi.2018014
[18]

Zhousheng Ruan, Sen Zhang, Sican Xiong. Solving an inverse source problem for a time fractional diffusion equation by a modified quasi-boundary value method. Evolution Equations & Control Theory, 2018, 7 (4) : 669-682. doi: 10.3934/eect.2018032
[19]

Loc H. Nguyen, Qitong Li, Michael V. Klibanov. A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media. Inverse Problems & Imaging, 2019, 13 (5) : 1067-1094. doi: 10.3934/ipi.2019048
[20]

Rua Murray. Approximation error for invariant density calculations. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 535-557. doi: 10.3934/dcds.1998.4.535

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences