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Issue 22, 2014
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Karhunen–Loève treatment to remove noise and facilitate data analysis in sensing, spectroscopy and other applications

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Abstract

Resolving weak spectral variations in the dynamic response of materials that are either dominated or excited by stochastic processes remains a challenge. Responses that are thermal in origin are particularly relevant examples due to the delocalized nature of heat. Despite its inherent properties in dealing with stochastic processes, the Karhunen–Loève expansion has not been fully exploited in measurement of systems that are driven solely by random forces or can exhibit large thermally driven random fluctuations. Here, we present experimental results and analysis of the archetypes (a) the resonant excitation and transient response of an atomic force microscope probe by the ambient random fluctuations and nanoscale photothermal sample response, and (b) the photothermally scattered photons in pump–probe spectroscopy. In each case, the dynamic process is represented as an infinite series with random coefficients to obtain pertinent frequency shifts and spectral peaks and demonstrate spectral enhancement for a set of compounds including the spectrally complex biomass. The considered cases find important applications in nanoscale material characterization, biosensing, and spectral identification of biological and chemical agents.

Graphical abstract: Karhunen–Loève treatment to remove noise and facilitate data analysis in sensing, spectroscopy and other applications

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Publication details

The article was received on 17 Jul 2014, accepted on 08 Sep 2014 and first published on 09 Sep 2014


Article type: Paper
DOI: 10.1039/C4AN01300J
Citation: Analyst, 2014,139, 5927-5935
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    Karhunen–Loève treatment to remove noise and facilitate data analysis in sensing, spectroscopy and other applications

    V. V. Zaharov, R. H. Farahi, P. J. Snyder, B. H. Davison and A. Passian, Analyst, 2014, 139, 5927
    DOI: 10.1039/C4AN01300J

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