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Asymptotic Behavior of Super-resolution Sparse Bayesian Learning

Shutin, Dmitriy (2024) Asymptotic Behavior of Super-resolution Sparse Bayesian Learning. IEEE. IEEE International Conference on Acoustics, Speech and Signal Processing, 2024-04-14 - 2024-04-19, Seoul, Südkorea. ISSN 1520-6149.

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Abstract

Sparse Bayesian Learning with dictionary refinement (SBL-DR) is a gridless technique for sparse signal reconstruction, focusing on super-resolution estimation of spectral line locations and their quantity. Its cost function coincides with that of stochastic maximum likelihood (SML), a well-known method in array processing for estimating frequencies of complex exponentials. While SML exhibits consistency and efficiency with growing array snapshots or size, SBL-DR faces inconsistency with only one measurement snapshot. This study explores SBL-DR asymptotic behavior using a single measurement snapshot and growing sample size using Gamma-convergence theory. It computes upper and lower bounds for the SBL-DR cost function, showing their convergence to a Gamma-limit that is minimized at true signal locations. By leveraging the properties of Gamma-convergence, it is established that the minima of the SBL-DR cost function asymptotically approach those of the Gamma-limit function, thereby achieving consistency for SBL-DR.

Item URL in elib:https://elib.dlr.de/202757/
Document Type:Conference or Workshop Item (Poster)
Title:Asymptotic Behavior of Super-resolution Sparse Bayesian Learning
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Shutin, DmitriyUNSPECIFIEDhttps://orcid.org/0000-0002-6065-6453UNSPECIFIED
Date:April 2024
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Publisher:IEEE
ISSN:1520-6149
Status:Accepted
Keywords:Sparse Bayesian learning, super-resolution, sparsity, Gamma-convergence
Event Title:IEEE International Conference on Acoustics, Speech and Signal Processing
Event Location:Seoul, Südkorea
Event Type:international Conference
Event Start Date:14 April 2024
Event End Date:19 April 2024
Organizer:IEEE
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:Digitalisation
DLR - Program:D IAS - Innovative Autonomous Systems
DLR - Research theme (Project):D - STARE
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Communications Systems
Deposited By: Shutin, Dmitriy
Deposited On:15 Feb 2024 17:51
Last Modified:24 Apr 2024 21:02

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