Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems

Authors:
Eldad Haber;Zhuojun Magnant;Christian Lucero;Luis Tenorio
Affiliations:
Department of Mathematics and Earth and Ocean Science, The University of British Columbia, Vancouver, Canada;Department of Mathematics and Computer Science, Emory University, Atlanta, USA;Department of Mathematical and Computer Science, Colorado School of Mines, Golden, USA;Department of Mathematical and Computer Science, Colorado School of Mines, Golden, USA
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

We consider the problem of experimental design for linear ill-posed inverse problems. The minimization of the objective function in the classic A-optimal design is generalized to a Bayes risk minimization with a sparsity constraint. We present efficient algorithms for applications of such designs to large-scale problems. This is done by employing Krylov subspace methods for the solution of a subproblem required to obtain the experiment weights. The performance of the designs and algorithms is illustrated with a one-dimensional magnetotelluric example and an application to two-dimensional super-resolution reconstruction with MRI data.