  We study Sigma-Delta quantization methods coupled with appropriate
reconstruction algorithms for digitizing randomly sampled low-rank matrices. We
show that the reconstruction error associated with our methods decays
polynomially with the oversampling factor, and we leverage our results to
obtain root-exponential accuracy by optimizing over the choice of quantization
scheme. Additionally, we show that a random encoding scheme, applied to the
quantized measurements, yields a near-optimal exponential bit-rate. As an added
benefit, our schemes are robust both to noise and to deviations from the
low-rank assumption. In short, we provide a full generalization of analogous
results, obtained in the classical setup of bandlimited function acquisition,
and more recently, in the finite frame and compressed sensing setups to the
case of low-rank matrices sampled with sub-Gaussian linear operators. Finally,
we believe our techniques for generalizing results from the compressed sensing
setup to the analogous low-rank matrix setup is applicable to other
quantization schemes.
