Compressed sensing (CS) is used to extract information that is sparsely distributed, where sparsity is a discrete concept, referring to the number of non-zero components in some basis.We show that CS is an effective strategy for estimating continuous-valued parameters from data corrupted by AWGN. CS based on naive discretization of parameters suffers performance loss due to basis mismatch. We show that basis mismatch is not an inherent limitation of CS by identifying isometries required to preserve estimation theoretic quantities like the ZZB and the CRB.Under such isometries, the effect of taking fewer measurements is merely an SNR penalty that depends only on the number of measurements. We show that the threshold behavior of the ZZB can then be used to predict the number of measurements.