Gridless compressive-sensing methods for frequency estimation: Points of tangency and links to basics
Gridless compressive-sensing methods for frequency estimation: Points of tangency and links to basics
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发表时间：
2014-11
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通讯作者：
P. Stoica;Gongguo Tang;Zai Yang;D. Zachariah
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作者：
P. Stoica;Gongguo Tang;Zai Yang;D. Zachariah
无网格压缩传感方法形成了最近提出的用于从噪声测量中估计正弦信号频率的一类方法。在本文中，我们回顾这些方法的主要目标是提供新的见解，它们之间的关系和他们的联系的基本方法的非线性最小二乘（NLS）。我们表明，一个凸松弛惩罚NLS导致原子范数最小化方法。这种方法又可以近似的SPICE方法，其中的对偶问题被证明是等效的全局匹配滤波器方法的无网格版本。
The gridless compressive-sensing methods form the most recent class of approaches that have been proposed for estimating the frequencies of sinusoidal signals from noisy measurements. In this paper we review these methods with the main goal of providing new insights into the relationships between them and their links to the basic approach of nonlinear least squares (NLS).We show that a convex relaxation of penalized NLS leads to the atomic-norm minimization method. This method in turn can be approximated by a gridless version of the SPICE method, for which the dual problem is shown to be equivalent to the global matched filter method.