A Novel Bayesian Approach for the Two-Dimensional Harmonic Retrieval Problem

TL;DR

This paper introduces a new Bayesian method for two-dimensional harmonic retrieval that improves parameter pairing and reduces computational complexity, effectively estimating harmonic components in challenging scenarios.

Contribution

A novel Bayesian approach with reparameterization and block sparsity modeling for 2D harmonic retrieval, enhancing accuracy and efficiency.

Findings

The H-MSBL algorithm accurately estimates harmonic components.

The method handles challenging scenarios without source identifiability issues.

Computational complexity remains low despite increased problem dimensionality.

Abstract

Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two dimensional harmonic retrieval problem, through remodeling and reparameterization of the standard data model. This new model allows us to introduce a block sparsity structure in a manner that enables a natural pairing of the parameters in the two dimensions. The numerical simulations demonstrate that the inference algorithm developed (H-MSBL) does not suffer from source identifiability issues and is capable of estimating the harmonic components in challenging scenarios, while maintaining a low computational complexity.