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Can we use PCA to detect small signals in noisy data?
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.ORCID iD: 0000-0002-6550-0087
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.ORCID iD: 0000-0002-0074-1349
2017 (English)In: Ultramicroscopy, ISSN 0304-3991, E-ISSN 1879-2723, Vol. 172, p. 40-46Article in journal (Refereed) Published
Abstract [en]

Principal component analysis (PCA) is among the most commonly applied dimension reduction techniques suitable to denoise data. Focusing on its limitations to detect low variance signals in noisy data, we discuss how statistical and systematical errors occur in PCA reconstructed data as a function of the size of the data set, which extends the work of Lichtert and Verbeeck, (2013) [16]. Particular attention is directed towards the estimation of bias introduced by PCA and its influence on experiment design. Aiming at the denoising of large matrices, nullspace based denoising (NBD) is introduced.

Place, publisher, year, edition, pages
2017. Vol. 172, p. 40-46
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-348242DOI: 10.1016/j.ultramic.2016.10.008ISI: 000390600200005PubMedID: 27794219OAI: oai:DiVA.org:uu-348242DiVA, id: diva2:1196948
Funder
Swedish Research CouncilThe Swedish Foundation for International Cooperation in Research and Higher Education (STINT)Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologyAvailable from: 2018-04-11 Created: 2018-04-11 Last updated: 2018-09-06Bibliographically approved
In thesis
1. Signal Processing Tools for Electron Microscopy
Open this publication in new window or tab >>Signal Processing Tools for Electron Microscopy
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The detection of weak signals in noisy data is a problem which occurs across various disciplines. Here, the signal of interest is the spectral signature of the electron magnetic chiral dichroism (EMCD) effect. In principle, EMCD allows for the measurement of local magnetic structures in the electron microscope, its spatial resolution, versatility and low hardware requirements giving it an eminent position among competing measurement techniques. However, experimental shortcomings as well as intrinsically low signal to noise ratio render its measurement challenging to the present day.   

This thesis explores how posterior data processing may aid the analysis of various data from the electron microscope. Following a brief introduction to different signals arising in the microscope and a yet briefer survey of the state of the art of EMCD measurements, noise removal strategies are presented. Afterwards, gears are shifted to discuss the separation of mixed signals into their physically meaningful source components based on their assumed mathematical characteristics, so called blind source separation (BSS).    

A data processing workflow for detecting weak signals in noisy spectra is derived from these considerations, ultimately culminating in several demonstrations of the extraction of EMCD signals. While the focus of the thesis does lie on data processing strategies for EMCD detection, the approaches presented here are similarly applicable in other situations. Related topics such as the general analysis of hyperspectral images using BSS methods or the fast analysis of large data sets are also discussed.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2018. p. 60
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1672
National Category
Physical Sciences Computer Sciences Other Mathematics
Identifiers
urn:nbn:se:uu:diva-348264 (URN)978-91-513-0345-1 (ISBN)
Public defence
2018-06-12, Å2001, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:00 (English)
Opponent
Supervisors
Available from: 2018-05-18 Created: 2018-04-11 Last updated: 2018-10-08

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