The use of self-adaptive principal components in PCA-based denoising

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10508734" target="_blank" >RIV/00216208:11320/25:10508734 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=yrzwXTCDwx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=yrzwXTCDwx</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmr.2024.107824" target="_blank" >10.1016/j.jmr.2024.107824</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The use of self-adaptive principal components in PCA-based denoising

Popis výsledku v původním jazyce

PCA-based denoising usually implies either discarding a number of high-index principal components (PCs) of a data matrix or their attenuation according to a regularization model. This work introduces an alternative, model- free, approach to high-index PC attenuation that seeks to average values of PC vectors as if they were expected from noise perturbation of data. According to the perturbation theory, the average PCs are attenuated versions of the clean PCs of noiseless data - the higher the noise-related content in a PC vector, the lower is its average&apos;s norm. This enables a regularization of the PC expansion of data where the PC terms are self-adapted to their noise content. To approximate the average PC vectors, the data matrix is randomly sampled several times to obtain numerous pseudo-random PC sets. The PCs of same ranks are then used to reconstruct the full-data PCs of that rank. A numerical algorithm of the reconstruction and its implementation in Python are provided. The proposed automatic adaptation to data offers a convenient solution for those who face with a problem of scaling or discarding PCs in PCA-based denoising. Questions of optimal sampling schedule and sampling amount remain issues that future work must address.

Název v anglickém jazyce

The use of self-adaptive principal components in PCA-based denoising

Popis výsledku anglicky

PCA-based denoising usually implies either discarding a number of high-index principal components (PCs) of a data matrix or their attenuation according to a regularization model. This work introduces an alternative, model- free, approach to high-index PC attenuation that seeks to average values of PC vectors as if they were expected from noise perturbation of data. According to the perturbation theory, the average PCs are attenuated versions of the clean PCs of noiseless data - the higher the noise-related content in a PC vector, the lower is its average&apos;s norm. This enables a regularization of the PC expansion of data where the PC terms are self-adapted to their noise content. To approximate the average PC vectors, the data matrix is randomly sampled several times to obtain numerous pseudo-random PC sets. The PCs of same ranks are then used to reconstruct the full-data PCs of that rank. A numerical algorithm of the reconstruction and its implementation in Python are provided. The proposed automatic adaptation to data offers a convenient solution for those who face with a problem of scaling or discarding PCs in PCA-based denoising. Questions of optimal sampling schedule and sampling amount remain issues that future work must address.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10302 - Condensed matter physics (including formerly solid state physics, supercond.)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Magnetic Resonance

ISSN

1090-7807

e-ISSN

1096-0856

Svazek periodika

371

Číslo periodika v rámci svazku

FEB

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

6

Strana od-do

107824

Kód UT WoS článku

001412331800001

EID výsledku v databázi Scopus

2-s2.0-85213251972