An RIP-Based Approach to $\Sigma \Delta $ Quantization for Compressed Sensing

In this letter, we provide a new approach to estimating the error of reconstruction from ΣΔ quantized compressed sensing measurements. Our method is based on the restricted isometry property (RIP) of a certain projection of the measurement matrix. Our result yields simple proofs and a slight generalization of the best-known reconstruction error bounds for Gaussian and subGaussian measurement matrices.