A MATLAB implementation of the minimum relative entropy method for linear inverse problems

Abstract

The minimum relative entropy (MRE) method can be used to solve linear inverse problems of the form Gm = d , where m is a vector of unknown model parameters and d is a vector of measured data. The MRE method treats the elements of m as random variables, and obtains a multivariate probability density function for m . The probability density function is constrained by prior information about the upper and lower bounds of m , a prior expected value of m , and the measured data. The solution of the inverse problem is the expected value of m , based on the derived probability density function. We present a MATLAB implementation of the MRE method. Several numerical issues arise in the implementation of the MRE method and are discussed here. We present the source history reconstruction problem from groundwater hydrology as an example of the MRE implementation.