SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information Part 1-Methodology
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SIPPI : A Matlab toolbox for sampling the solution to inverse problems with complex prior information Part 1-Methodology. / Hansen, Thomas Mejer; Cordua, Knud Skou; Looms, Majken Caroline; Mosegaard, Klaus.
I: Computers & Geosciences, Bind 52, 01.03.2013, s. 470-480.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - SIPPI
T2 - A Matlab toolbox for sampling the solution to inverse problems with complex prior information Part 1-Methodology
AU - Hansen, Thomas Mejer
AU - Cordua, Knud Skou
AU - Looms, Majken Caroline
AU - Mosegaard, Klaus
PY - 2013/3/1
Y1 - 2013/3/1
N2 - From a probabilistic point-of-view, the solution to an inverse problem can be seen as a combination of independent states of information quantified by probability density functions. Typically, these states of information are provided by a set of observed data and some a priori information on the solution. The combined states of information (i.e. the solution to the inverse problem) is a probability density function typically referred to as the a posteriori probability density function. We present a generic toolbox for Matlab and Gnu Octave called SIPPI that implements a number of methods for solving such probabilistically formulated inverse problems by sampling the a posteriori probability density function. In order to describe the a priori probability density function, we consider both simple Gaussian models and more complex (and realistic) a priori models based on higher order statistics. These a priori models can be used with both linear and non-linear inverse problems. For linear inverse Gaussian problems we make use of least-squares and kriging-based methods to describe the a posteriori probability density function directly. For general nonlinear (i.e. non-Gaussian) inverse problems, we make use of the extended Metropolis algorithm to sample the a posteriori probability density function. Together with the extended Metropolis algorithm, we use sequential Gibbs sampling that allow computationally efficient sampling of complex a priori models. The toolbox can be applied to any inverse problem as long as a way of solving the forward problem is provided. Here we demonstrate the methods and algorithms available in SIPPI. An application of SIPPI, to a tomographic cross borehole inverse problems, is presented in a second part of this paper. (C) 2012 Elsevier Ltd. All rights reserved.
AB - From a probabilistic point-of-view, the solution to an inverse problem can be seen as a combination of independent states of information quantified by probability density functions. Typically, these states of information are provided by a set of observed data and some a priori information on the solution. The combined states of information (i.e. the solution to the inverse problem) is a probability density function typically referred to as the a posteriori probability density function. We present a generic toolbox for Matlab and Gnu Octave called SIPPI that implements a number of methods for solving such probabilistically formulated inverse problems by sampling the a posteriori probability density function. In order to describe the a priori probability density function, we consider both simple Gaussian models and more complex (and realistic) a priori models based on higher order statistics. These a priori models can be used with both linear and non-linear inverse problems. For linear inverse Gaussian problems we make use of least-squares and kriging-based methods to describe the a posteriori probability density function directly. For general nonlinear (i.e. non-Gaussian) inverse problems, we make use of the extended Metropolis algorithm to sample the a posteriori probability density function. Together with the extended Metropolis algorithm, we use sequential Gibbs sampling that allow computationally efficient sampling of complex a priori models. The toolbox can be applied to any inverse problem as long as a way of solving the forward problem is provided. Here we demonstrate the methods and algorithms available in SIPPI. An application of SIPPI, to a tomographic cross borehole inverse problems, is presented in a second part of this paper. (C) 2012 Elsevier Ltd. All rights reserved.
KW - Inversion
KW - Nonlinear
KW - Sampling
KW - A priori
KW - A posteriori
KW - SIMULATION
U2 - 10.1016/j.cageo.2012.09.004
DO - 10.1016/j.cageo.2012.09.004
M3 - Journal article
VL - 52
SP - 470
EP - 480
JO - Computers & Geosciences
JF - Computers & Geosciences
SN - 0098-3004
ER -
ID: 335428395