TITLE:
Imaging Applications with Variable Projections
AUTHORS:
Victor Pereyra, Godela Scherer
KEYWORDS:
Medical Imaging, Geophysics, Variable Projections, Nonlinear Least Squares
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.9 No.4,
December
16,
2019
ABSTRACT: We review two important fields of application for the method of Variable Projections (VARPRO): Seismic Prospecting and Medical Imaging. We cover the period since 2002 when a first review was published. Variable Projections is a method for the solution of nonlinear least squares problems where the model is a linear combination of nonlinear functions. Its success is based on the fact that the reduced functional, where the linear parameters are eliminated converges always faster than if the same method of solution is applied to the original problem. More importantly, many of these problems are very hard to solve in their original format and VARPRO has shown its value in many different applications.