Finite-dimensional approximation of the inverse frame operator

A frame in a Hilbert space H allows every element in H to be written as a l inear combination of the frame elements, with coefficients called frame coe fficients. Calculations of those coefficients and many other situations whe re frames occur, requires knowledge of the inverse frame operator. But usua lly it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce a method for ap proximation of the inverse frame operator using finite subsets of the frame . In particular this allows to approximate the frame coefficients (even in l(2)-sense) using finite-dimensional linear algebra. We show that the gener al method simplifies in the important cases of Weil-Heisenberg frames and w avelet frames.