Spherical Harmonic Atomic Norm and its Application to DOA Estimation
Spherical Harmonic Atomic Norm and its Application to DOA Estimation
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DOI：
10.1109/access.2019.2950016
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发表时间：
2019-10
期刊：
影响因子：
3.9
通讯作者：
Jie Pan
中科院分区：
文献类型：
--
作者：
Jie Pan
球谐（SH）域中的信号处理具有在整个空间中以相等分辨率分析球上的信号以及分解信号的频率和位置相关分量的优点。因此，它发现最近的应用在信号恢复和定位。在本文中，我们考虑的无网格稀疏信号恢复问题的SH域原子范数最小化（ANM）。由于球面调和函数不具有Vandermonde结构，传统ANM方法的数学基础Vandermonde分解定理在SH域中不适用。为了解决这个问题，低维半定规划（SDP）的方法来实现球谐原子范数最小化（SH-ANM）的方法。该方法不依赖于Vandermonde分解，可以直接恢复SH域中的原子分解。作为应用，我们提出了基于所提出的SH-ANM方法的波达方向估计方法，计算机仿真表明，其性能优于国家的最先进的同行上级。此外，我们验证了在现实生活中的声学场景中的多个扬声器定位使用LACATA挑战的测量数据的结果。
Signal processing in the spherical harmonic (SH) domain has the advantages of analyzing a signal on the sphere with equal resolution in the whole space and of decomposite the frequency- and location-dependent components of the signal. Therefore, it finds recent applications in signal recovery and localization. In this paper, we consider the gridless sparse signal recovery problem in the SH domain with atomic norm minimization (ANM). Due to the absence of Vandermonde structure for spherical harmonics, the Vandermonde decomposition theorem, which is the mathematic foundation of conventional ANM approaches, is not applicable in the SH domain. To address this issue, a low-dimensional semidefinite programming (SDP) method to implement the spherical harmonic atomic norm minimization (SH-ANM) approach is proposed. This method does not rely on the Vandermonde decomposition and can recover the atomic decomposition in the SH domain directly. As an application, we develop the direction-of-arrival estimation approach based on the proposed SH-ANM method, and computer simulations demonstrate that its performance is superior to the state-of-the-art counterparts. Furthermore, we validate the results in real-life acoustics scenes for multiple speakers localization using measured data in LACATA challenge.