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.
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Haber, E., Magnant, Z., Lucero, C. et al. Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems. Comput Optim Appl 52, 293–314 (2012). https://doi.org/10.1007/s10589-011-9404-4
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DOI: https://doi.org/10.1007/s10589-011-9404-4