Memoryless scalar quantization for random frames

Memoryless scalar quantization (MSQ) is a common technique to quantize generalized linear samples of signals. The non-linear nature makes the analysis corresponding approximation error challenging, often resulting in use simplifying assumption, called “white noise hypothesis” (WNH) that useful, yet also known be not rigorous and, at least certain cases, valid. We obtain reconstruction estimates without relying on WNH setting where fixed deterministic signal are obtained using (the matrix of) random frame with independent isotropic sub-Gaussian rows; quantized MSQ; and reconstructed linearly. establish non-asymptotic bounds explain observed decay rate as number measurements grows, which special case Gaussian frames show approaches (small) non-zero constant lower bound. extend our methodology dithered noisy settings well compressed sensing we agree empirical observations, again, resorting WNH.