Subspace estimation under coarse quantization

We study subspace estimation from coarsly quantized data. In particular, we analyze two stochastic quantization schemes which use dithering: a one-bit quantizer combined with rectangular dither and a multi-bit quantizer with triangular dither. For each quantizer, we derive rigorous high probability bounds for the distances between the true and estimated signal subspaces. Using our analysis, we identify scenarios in which subspace estimation via triangular dithering qualitatively outperforms rectangular dithering. We verify in numerical simulations that our estimates are optimal in their dependence on the smallest non-zero eigenvalue of the target matrix.