The two-dimensional grid-free compressed sensing method with planar microphone arrays is expected to achieve super-resolution direction-of-arrival (DOA) estimation for acoustic sources in the hemispherical space in front of array. The existing methods are not yet well compatible with arbitrary planar array geometries. In this paper, we aim to break this limitation and explore a novel method applicable to arbitrary planar array geometries. First, the covariance between source-induced signals at arbitrary two microphones is formulated as related to the two-dimensional inverse Fourier transform of the source strength. Then, a mathematical model with a source sparsity constraint is built in the continuous domain to denoise the covariances of measured signals, which can be solved by decoupled positive semidefinite programming. Finally, the DOAs are extracted from the solution of the mathematical model via a matrix pencil and pairing method. Simulation and experimental results demonstrate the effectiveness of the proposed method.

平面麦克风阵列的二维无网格压缩感知方法有望实现阵列前方半球空间声源的超分辨率到达方向（DOA）估计。现有方法还不能很好地兼容任意平面阵列几何形状。在本文中，我们的目标是打破这一限制，探索一种适用于任意平面阵列几何形状的新方法。首先，将任意两个麦克风处的源感应信号之间的协方差公式化为与源强度的二维傅里叶逆变换相关。然后，在连续域中建立带有源稀疏性约束的数学模型，对测量信号的协方差进行去噪，并可以通过解耦正半定规划来求解。最后，通过矩阵铅笔和配对方法从数学模型的解中提取DOA。仿真和实验结果证明了该方法的有效性。