Emanuel Winterfors and Andrew Curtis 2008 Inverse Problems 24 025016 doi:10.1088/0266-5611/24/2/025016
Emanuel Winterfors1,2 and Andrew Curtis2,3
Show affiliationsWe present a novel approach to analyze uniqueness in nonlinear inverse problems, using a novel bifocal Newtonian algorithm for identifying pairs of non-unique solutions for any potential data set, prior to any data collection. For the case when the shape of the forward function depends on control parameters that can be tuned to reduce non-uniqueness, we present a second algorithm which minimizes the sum of squared distances between each pair of non-unique solutions. Both algorithms are also relevant in the presence of uncertainty, which we demonstrate by applying them to a simple nonlinear location problem.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
Issue 2 (April 2008)
Received 5 October 2007, in final form 21 January 2008
Published 21 February 2008
Emanuel Winterfors and Andrew Curtis 2008 Inverse Problems 24 025016
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