Quantization for Spectral Super-Resolution

被引:0
作者
Gunturk, C. Sinan [1 ]
Li, Weilin [1 ]
机构
[1] NYU, Courant Inst Math Sci, New York, NY 10003 USA
关键词
Quantization; Super-resolution; Spectral estimation; Total variation; ESPRIT; SIGMA-DELTA QUANTIZATION; FRAMES; FAMILY; LIMIT;
D O I
10.1007/s00365-022-09574-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 lambda as the largest integer such that left perpendicular M/X right perpendicular - 1 >= 4/Delta, where M denotes the number of Fourier measurements and Delta 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 lambda(5/4) K-lambda/2) and O(M-3/2 lambda(1/2) K-lambda), respectively, where the implicit constants are independent of M, K and lambda. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order O(M-1 K-1) only, regardless of the reconstruction algorithm.
引用
收藏
页码:619 / 648
页数:30
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