平面大筛子与时频表示的稀疏性
A planar large sieve and sparsity of time-frequency representations
摘要：
为了测量真实信号的稀疏性，Donoho和Logan引入了最大奈奎斯特密度的概念，并将其用于将Benneri的大筛原理扩展到带限函数。这导致了几个恢复算法的基础上的最小化的$L_{1}$规范。在本文中，我们引入了{\ planar maximum} Nyquist density的概念，它度量了一个函数的时间-频率分布的稀疏性。我们得到一个平面大筛原理，适用于具有高斯窗口的时频表示，或等效地，福克空间，$\mathcal{F}_{1}\left( \mathbb{C}\right) $，允许在调制空间$M_{1}$（也称为Feichtinger代数$S_{0}$）中的函数的短傅里叶变换（STFT）的稀疏噪声破坏的完美恢复，并在$M_{1}$中丢失的STFT数据的近似，通过$L_{1}$ -最小化。
英文摘要：
With the aim of measuring the sparsity of a real signal, Donoho and Logan introduced the concept of maximum Nyquist density, and used it to extend Bombieri's principle of the large sieve to bandlimited functions. This led to several recovery algorithms based on the minimization of the $L_{1}$-norm. In this paper we introduce the concept of {\ planar maximum} Nyquist density, which measures the sparsity of the time-frequency distribution of a function. We obtain a planar large sieve principle which applies to time-frequency representations with a gaussian window, or equivalently, to Fock spaces, $\mathcal{F}_{1}\left( \mathbb{C}\right) $, allowing for perfect recovery of the short-Fourier transform (STFT) of functions in the modulation space $M_{1}$ (also known as Feichtinger's algebra $S_{0}$) corrupted by sparse noise and for approximation of missing STFT data in $M_{1}$, by $L_{1}$-minimization.
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。
