A fast parametric modelling algorithm with the Powell method

Abstract

This paper presents a model that comprises only two parameters (R/S, fr) and the application of three function minimization algorithms (simplex, Powell and modified Powell) to this model to obtain parametric images. Comparisons among the three algorithms in terms of efficiency and reliability were carried out. It was found that, with proper initialization by taking the shape of the modelled data into consideration, the minimization function can be approximated by a quadratic function near the minimum point, therefore the iteration times can be minimized in the modified Powell method. The results show that with the modified Powell method a substantial reduction of computation time can be achieved in the parametric imaging. This makes it possible to obtain a 16 x 16 parametric image in 1 s.