Year: 2026
Type: preprint
Abstract: In this paper, we extend the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction for an arbitrary number of non-zero parameters. The topic touches on exact reconstructibility, most commonly studied in compressed sensing and multisource estimation across various imaging problems. The theoretical results derive upper bounds on the number of recoverable parameters in the noiseless case, and define a probability measure to assess the likelihood of recovering all non-zero parameters with correct magnitude order. The work provides a mathematical explanation of the open question regarding the noise robustness of standardized and unbiased methods. The paper also reveals a trade-off between the number of sensors and the signal-to-noise ratio. Numerical experiments demonstrate the theoretical findings.
Source: arXiv (Cornell University)
Author: Lahtinen, Joonas
Institutions: Tampere University, University of Tampere
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Opetus- ja Kulttuuriministeriö
OpenAlex ID: W7160647746