Estimating Inharmonic Signals with Optimal Transport Priors

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Abstract

In this work, we consider the problem of estimating the frequency content of inharmonic signals, i.e., sinusoidal mixtures whose components are close to forming a harmonic set. Intuitively, exploiting this closeness should lead to increased estimation performance as compared to unstructured estimation. Earlier approaches to this problem have relied on parametric descriptions of the inharmonicity, stochastic representations, or have resorted to misspecified estimation by ignoring the inharmonicity. Herein, we propose to use a penalized maximum-likelihood framework, where the regularizer is constructed based on optimal mass transport theory, promoting estimates that are close-to-harmonic in a spectral sense. This leads to an estimator that forms a smooth path between the unstructured maximum-likelihood estimator (MLE) and a misspecified MLE (MMLE), as determined by a regularization parameter. In numerical illustrations, we show that the proposed estimator worst-case dominates the MLE and MMLE, thereby allowing for robust estimation for cases when the inharmonicity level is unknown.
Original languageEnglish
Title of host publicationICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherIEEE
Pages1-5
Number of pages5
ISBN (Electronic)978-1-7281-6327-7
ISBN (Print)978-1-7281-6328-4
DOIs
Publication statusPublished - 10 Jun 2023
MoE publication typeA4 Conference publication
EventIEEE International Conference on Acoustics, Speech, and Signal Processing - Rhodes Island, Greece
Duration: 4 Jun 202310 Jun 2023

Publication series

NameProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
ISSN (Electronic)2379-190X

Conference

ConferenceIEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated titleICASSP
Country/TerritoryGreece
CityRhodes Island
Period04/06/202310/06/2023

Keywords

  • Maximum likelihood estimation
  • Signal processing
  • Harmonic analysis
  • Frequency estimation
  • Acoustics
  • Speech processing

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