The Bourgain-Tzafriri Restricted Invertibility Theorem states conditions under
which a Riesz bases (with controlled lower Riesz bound) can be extracted from a possibly overcomplete system of
vectors in finite dimensional spaces. We extend the result to vector dictionaries
in infinite dimensional Hilbert spaces using techniques developed in the theory of
localized frames, and describe possibilities of controlling the upper Riesz bound as well.