This paper presents a POCS-based algorithm for consistent reconstruction of a signal x in RK from any subset of quantized coefficients y in RN in an N by K overcomplete frame expansion y = Fx, N = 2K. By choosing the frame operator F to be the concatenation of two K by K invertible transforms, the projections may be computed in RK using only the transforms and their inverses, rather than in the larger space RN using the pseudo-inverse as proposed in earlier work. This enables practical reconstructions from overcomplete frame expansions based on wavelet, subband, or lapped transforms of an entire image, which has heretofore not been possible.