Non-convexly constrained linear inverse problems
It generalizes sparsity-constrained inversion to broader non-convex constraints in infinite-dimensional settings, which is incremental for researchers in inverse problems.
This paper extends the inversion of ill-posed linear operators with non-convex constraints from finite dimensions to Hilbert spaces, providing theoretical stability guarantees and an iterative algorithm.
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.