Inverse Photon Transport : Space Science Applications

This paper is focused on the application of inverse problem methodology for solving some problems that have emerged in space science. The inverse model is an implicit technique: a constrained non-linear optimization problem, in which the forward problem is iteratively solved for successive approximations of the unknown parameters. Iteration proceeds until an objective-function, representing the least-square fit of model results and experimental data added to a regularization term, converges to a specified small value. 1. FORMULATION OF THE INVERSE PROBLEM A technique for property reconstruction from measurements can be described as a generalized least squares approximation. The standard least squares solution can be unstable in the presence of noise. In order to have a robust inverse model, assuring that parameter variation is bounded to become the final solution physically acceptable, some a priori information must be added to the quadratic difference term. In general, this additional information associated to the inverse solution means smoothness. Denoting by p = [ p1, p2, . . . , pNp ]T the unknown vector to be determined by the inverse analysis, the inverse problem can be formulated as a nonlinear optimization problem, min J(p) , lq ≤ pq ≤ uq , q = 1, . . . , Np , (1) where the lower and upper bounds lq and uq are chosen in order to allow the inversion to lie within some known physical limits, and the objective function is given by