  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 is projected as independent univariate von
Mises distribution to perform tractable inference. Besides, for the
initialization, efficient fast Fourier transform (FFT) is adopted to
significantly reduce the computation complexity of MDVALSE. Numerical results
demonstrate the effectiveness of the MDVALSE, compared to state-of-art methods.
