The fundamental multidimensional line spectral estimation problem is addressed utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) algorithm, multidimensional VALSE (MDVALSE) is developed. MDVALSE inherits the advantages of VALSE such as automatically estimating the model order, noise variance and providing uncertain degrees of frequency estimates. Compared to VALSE, the multidimensional frequencies of a single component is treated as a whole, and the probability density function (PDF) is projected as independent univariate von Mises distribution to perform tractable inference. Besides, for the initialization, efficient fast Fourier transform (FFT) is adopted to approximate the marginal posterior PDF of frequencies. Numerical results demonstrate the effectiveness of the MDVALSE, compared to state-of-art methods.

中文翻译：

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多维变分线谱估计

利用贝叶斯方法解决了基本的多维线谱估计问题。受最近提出的变分线谱估计 (VALSE) 算法的启发，开发了多维 VALSE (MDVALSE)。MDVALSE 继承了 VALSE 的优点，如自动估计模型阶数、噪声方差和提供频率估计的不确定度。与 VALSE 相比，将单个分量的多维频率视为一个整体，将概率密度函数 (PDF) 投影为独立的单变量 von Mises 分布以进行易处理的推理。此外，对于初始化，采用高效的快速傅立叶变换 (FFT) 来近似频率的边缘后验 PDF。数值结果证明了 MDVALSE 的有效性，