Non-convexly constrained linear inverse problems

Details Non-convexly constrained linear inverse problems Non-convexly constrained linear inverse problems

2009-11-26

arxiv.org/abs/0911.5098v1

Mathematics

Numerical Analysis

Scientific paper

This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin to the projected Landweber algorithm is studied. This work extends recent progress made on the efficient inversion of finite dimensional linear systems under a sparsity constraint to the Hilbert space setting and to more general non-convex constraints.

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