# SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information

- Authors:
- Subtitle:
- Part 1â€”Methodology
- DOI:
- 10.1016/j.cageo.2012.09.004
- Abstract:
- 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 non-linear (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.
- Type:
- Journal article
- Language:
- English
- Published in:
- Computers and Geosciences, 2013, Vol 52, p. 470-480
- Keywords:
- Inversion; Nonlinear; Sampling; A priori; A posteriori
- Main Research Area:
- Science/technology
- Publication Status:
- Published
- Review type:
- Peer Review
- Submission year:
- 2013
- Scientific Level:
- Scientific
- ID:
- 235264496