On Unbiased Parameter Estimation and Signal Reconstruction
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.
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BibTeX
@misc{lahtinen2026unbiased,
title = {{On Unbiased Parameter Estimation and Signal Reconstruction}},
author = {Joonas Lahtinen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.05276},
eprint = {2605.05276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.05276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Unbiased Parameter Estimation and Signal Reconstruction
AU - Joonas Lahtinen
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2605.05276
UR - https://arxiv.org/abs/2605.05276
AB - 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.
ER -