一种基于压缩感知的无需超参数的测向算法

A Hyperparameter-Free Direction-Finding Algorithm in the Compressive Sensing Framework

全自动的稀疏参数估计算法不需要用户对于超参数的数值做出任何艰难的决定(可能是试错而来),因而更加实用。本文给出了现有方法的统一阐释,包括协方差矩阵拟合(CMF)、基于稀疏迭代协方差的估计(SPICE)以及基于似然的稀疏参数估计(LIKES),认为它们全部都是不同统计距离下的基于协方差矩阵拟合的方法。在此基础上,本文提出了一种新的协方差矩阵拟合方案,将两种非对称Itakura-Saito距离的其中一种最小化。计算机仿真表明,本文提出方法相比上述方法的性能具有优势。

The fully automatic sparsity-parameter estimation algorithms do not require the user to make any hard decision (possibly via trial-and-error) on the values of the hyperparameters, making them more pragmatic in practice. This paper provides a unified interpretation of the existing approaches including covariance matrix fitting (CMF), sparse iterative covariance based estimation (SPICE) and likelihood-based estimation of sparse parameters (LIKES). The point of view taken is that they are all covariance-fitting-based algorithms under different statistical distances. Following this, we present a new covariance-fitting scheme trying to minimize one of the two asymmetrical Itakura-Saito distances. Simulations show that the proposed method appears to be preferable as it outperforms the aforementioned algorithms in general.