DeepAI AI Chat
Log In Sign Up

Variational Bayesian Inference of Line Spectra

by   Mihai-Alin Badiu, et al.
Aalborg University

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cramér-Rao bound computed for the true model order.


page 1

page 2

page 3

page 4


Variational Bayesian Inference of Line Spectral Estimation with Multiple Measurement Vectors

In this paper, the line spectral estimation (LSE) problem with multiple ...

Multidimensional Variational Line Spectra Estimation

The fundamental multidimensional line spectral estimation problem is add...

Boosting Variational Inference

Variational inference (VI) provides fast approximations of a Bayesian po...

Bayesian Nonparametric Spectral Estimation

Spectral estimation (SE) aims to identify how the energy of a signal (e....

Variational Inference of Dynamic Factor Models with Arbitrary Missing Data

Dynamic factor models are often estimated by point-estimation methods, d...

Sparse Horseshoe Estimation via Expectation-Maximisation

The horseshoe prior is known to possess many desirable properties for Ba...

Off-grid Variational Bayesian Inference of Line Spectral Estimation from One-bit Samples

In this paper, the line spectral estimation (LSE) problem is studied fro...