{"title":"The use of self-adaptive principal components in PCA-based denoising","authors":"Oleg V. Petrov","doi":"10.1016/j.jmr.2024.107824","DOIUrl":null,"url":null,"abstract":"<div><div>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’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.</div></div>","PeriodicalId":16267,"journal":{"name":"Journal of magnetic resonance","volume":"371 ","pages":"Article 107824"},"PeriodicalIF":2.0000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of magnetic resonance","FirstCategoryId":"92","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1090780724002088","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
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’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.
期刊介绍:
The Journal of Magnetic Resonance presents original technical and scientific papers in all aspects of magnetic resonance, including nuclear magnetic resonance spectroscopy (NMR) of solids and liquids, electron spin/paramagnetic resonance (EPR), in vivo magnetic resonance imaging (MRI) and spectroscopy (MRS), nuclear quadrupole resonance (NQR) and magnetic resonance phenomena at nearly zero fields or in combination with optics. The Journal''s main aims include deepening the physical principles underlying all these spectroscopies, publishing significant theoretical and experimental results leading to spectral and spatial progress in these areas, and opening new MR-based applications in chemistry, biology and medicine. The Journal also seeks descriptions of novel apparatuses, new experimental protocols, and new procedures of data analysis and interpretation - including computational and quantum-mechanical methods - capable of advancing MR spectroscopy and imaging.