Title: Separable nonlinear least squares fitting with linear bound constraints and its application in magnetic resonance spectroscopy data quantification
Authors: Sima, Diana ×
Van Huffel, Sabine #
Issue Date: Jun-2007
Publisher: Elsevier
Series Title: Journal of Computational and Applied Mathematics vol:203 issue:1 pages:264-278
Abstract: An application in magnetic resonance spectroscopy quantification models a signal as a linear combination of nonlinear functions. It leads to a separable nonlinear least squares fitting problem. with linear bound constraints on some variables. The variable projection (VARPRO) technique can be applied to this problem, but needs to be adapted in several respects. If only the nonlinear variables are subject to constraints, then the Levenberg-Marquardt minimization algorithm that is classically used by the VARPRO method should be replaced with a version that can incorporate those constraints. If some of the linear variables are also constrained, then they cannot be projected out via a closed-form expression as is the case for the classical VARPRO technique. We show how quadratic programming problems can be solved instead, and we provide details on efficient function and approximate Jacobian evaluations for the inequality constrained VARPRO method. (c) 2006 Elsevier B.V. All rights reserved.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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