Random sampling and reconstruction of concentrated signals in a reproducing kernel space

In this paper, we consider (random) sampling of signals concentrated on a bounded Corkscrew domain ? metric measure space, and reconstructing approximately from their (un)corrupted data taken set contained in ?. We establish weighted stability bi-Lipschitz type for scheme the reproducing kernel space. The provides weak robustness to scheme, however due nonconvexity signals, it does not imply unique signal reconstruction. From samples finite ?, propose an algorithm find approximations Random is where positions are randomly according probability distribution. Next show that, with high probability, can be reconstructed uncorrupted (or corrupted) at i.i.d. random drawn provided that size least order ?(?)ln?(?(?)), ?(?) Finally, demonstrate performance proposed original when procedure either large density or size.