arXiv 2103.000792021-03cs.ITmath.IT

用于光谱超分辨率的Quantization

Quantization for spectral super-resolution

C. Sinan Güntürk, Weilin Li

备注：: 29 pages, 2 figures, to appear in Constructive Approximation

摘要：

我们表明，分布式噪声整形β量化的方法提供了优越的性能的频谱超分辨率与量化的问题时，有冗余的测量数量。更准确地说，我们将过采样率$λ$定义为使得$\lfloor M/λ\rfloor - 1\geq 4/Δ$的最大整数，其中$M$表示傅立叶测量的数量，并且$Δ$是与要解析的原子测量相关联的最小分离距离。我们证明，对于任何数量的$K\geq 2$的量化水平可用于测量的实部和虚部，我们的量化方法结合TV-min/BLASSO或ESPRIT保证重建精度的顺序分别为$O(M^{1/4}λ^{5/4} K^{- λ/2})$和$O(M^{3/2} λ^{1/2} K^{- λ})$，其中的隐式常数是独立的$M$，$K$和$λ$。相比之下，对于相同字母表的朴素舍入或无记忆标量量化仅提供阶数$O(M^{-1}K^{-1})$的保证，而不管重构算法。

英文摘要：

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 $λ$ as the largest integer such that $\lfloor M/λ\rfloor - 1\geq 4/Δ$, 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 $K\geq 2$ 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 $O(M^{-1}K^{-1})$ only, regardless of the reconstruction algorithm.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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