  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.
