Papers › Quantization for spectral super-resolution
Quantization for spectral super-resolution
C. Sinan Güntürk, Weilin Li
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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, we define the oversampling ratio λ as the largest integer such that ⌊M/λ⌋- 1≥4/Δ, where M denotes the number of Fourier measurements and Δ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number K≥2 of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order O(M^(1/4)λ^(5/4) K^(- λ/2)) and O(M^(3/2) λ^(1/2) K^(- λ)) respectively, where the implicit constants are independent of M, K and λ. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order O(M⁻¹K⁻¹) only, regardless of the reconstruction algorithm.
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