1 research outputs found
Estimating Nuisance Parameters in Inverse Problems
Many inverse problems include nuisance parameters which, while not of direct
interest, are required to recover primary parameters. Structure present in
these problems allows efficient optimization strategies - a well known example
is variable projection, where nonlinear least squares problems which are linear
in some parameters can be very efficiently optimized. In this paper, we extend
the idea of projecting out a subset over the variables to a broad class of
maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with
nuisance parameters, such as variance or degrees of freedom. As a result, we
are able to incorporate nuisance parameter estimation into large-scale
constrained and unconstrained inverse problem formulations. We apply the
approach to a variety of problems, including estimation of unknown variance
parameters in the Gaussian model, degree of freedom (d.o.f.) parameter
estimation in the context of robust inverse problems, automatic calibration,
and optimal experimental design. Using numerical examples, we demonstrate
improvement in recovery of primary parameters for several large- scale inverse
problems. The proposed approach is compatible with a wide variety of algorithms
and formulations, and its implementation requires only minor modifications to
existing algorithms.Comment: 16 pages, 5 figure