A projection onto convex sets (POCS)-based method for consistent reconstruction of a signal from a subset of quantized coefficients received from an N.times.K overcomplete transform. By choosing a frame operator F to be the concatenization of two or more K.times.K invertible transforms, the POCS projections are calculated in R.sup.K space using only the K.times.K transforms and their inverses, rather than the larger R.sup.N space using pseudo inverse transforms. Practical reconstructions are enabled based on, for example, wavelet, subband, or lapped transforms of an entire image. In one embodiment, unequal error protection for multiple description source coding is provided. In particular, given a bit-plane representation of the coefficients in an overcomplete representation of the source, one embodiment of the present invention provides coding the most significant bits with the highest redundancy and the least significant bits with the lowest redundancy. In one embodiment, this is accomplished by varying the quantization stepsize for the different coefficients. Then, the available received quantized coefficients are decoded using a method based on alternating projections onto convex sets.