Multidimensional Variational Line Spectra Estimation

TL;DR

This paper introduces MDVALSE, a Bayesian method for multidimensional line spectral estimation that automatically estimates model parameters and treats multidimensional frequencies holistically, with improved computational efficiency.

Contribution

The paper develops MDVALSE, extending VALSE to multidimensional data, incorporating a new inference approach, and utilizing FFT for faster computation.

Findings

MDVALSE accurately estimates model order and noise variance.

It effectively handles multidimensional frequency estimation.

Numerical results outperform state-of-the-art methods.

Abstract

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.