Non-convexly constrained linear inverse problems

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Description/Abstract

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