High-performance quantization for spectral super-resolution

We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, if the (integer) oversampling ratio λ is such that lfloorM/λ rfloor - 1 ≥ 4/Δ, where M denotes the number of Fourier measurements and is the minimum separation distance associated with the atomic measure to be resolved, then for any number K ≥ 2 of quantization levels available for the real and imaginary parts of the measurements, our quantization method guarantees reconstruction accuracy of order O(λ^3/2 K^-λ/2), up to constants which are independent of K and λ. In contrast, memoryless scalar quantization offers a guarantee of order O(K^-1) only.