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

The minimum relative entropy (MRE) method can be used to solve linear inver se problems of the form Gm = d, where m is a vector of unknown model parame ters 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 f unction for m. The probability density Function is constrained by prior inf ormation 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 expecte d 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. (C) 2001 Elsevier Science Ltd. All right s reserved.