Quantization for Spectral Super-Resolution

We show that the method of distributed noise-shaping beta-quantization offers superior performance for problem spectral super-resolution with quantization whenever there is redundancy in number measurements. More precisely, we define over-sampling ratio $$\lambda $$ as largest integer such $$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta , where M denotes Fourier measurements and $$\Delta minimum separation distance associated atomic measure to be resolved. prove any $$K\ge 2$$ levels available real imaginary parts measurements, our combined either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy order $$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})$$ $$O(M^{3/2} ^{1/2} })$$ respectively, implicit constants are independent M, K . In contrast, naive rounding memoryless scalar same alphabet a guarantee $$O(M^{-1}K^{-1})$$ only, regardless algorithm.