Algorithm for optimal denoising of Raman spectra

Barton, Sinead J.; Ward, Tomás E.; Hennelly, Bryan M.

doi:10.1039/c8ay01089g

Cited by 75 publications

(70 citation statements)

References 19 publications

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“…Noise in spectroscopic data acquired with a nonintensified charge coupled device consists of Poisson noise (shot and thermal noise) and Gaussian noise (readout noise). However, above certain noise levels, Gaussian noise is a good approximation for Poisson noise . The sum of a mutually independent zero‐mean Gaussian noise is still a zero‐mean Gaussian noise with variance equal to the sum of the variances of the independent Gaussian noises .…”

Section: Methodsmentioning

confidence: 99%

“…The sum of a mutually independent zero‐mean Gaussian noise is still a zero‐mean Gaussian noise with variance equal to the sum of the variances of the independent Gaussian noises . Thus, spectroscopic noise can be modelled as the summation

N_{sim} ((), x_{i}) = e ((), x_{i}) \sqrt{{n_{italicph}}^{2} ((), x_{i}) + {n_{italicth}}^{2} + {n_{italicrd}}^{2}}

of shot noise n ph (also referred to as photon noise), thermal noise n th , and readout noise n rd . e ( x i ) is Gaussian noise having a standard deviation of one and mean of zero .…”

Section: Methodsmentioning

confidence: 99%

“…The noise‐reduced spectrum r ( x i ) results after noise reduction from either the simulated or the experimental spectra R ( x i ) with either the vector casting method, the envelope‐finder method, the SG method, or the wavelet transform method. In order to compare the performance of the different noise reduction methods, we quantified the deviation between the real signal spectrum S sig ( x i ) and the noise‐reduced spectra r ( x i ) derived with the different methods according to Equations to as proposed by Barton et al These equations quantify (a) the mean improvement of the signal quality across the entire spectral range (Equation ), (b) monitor whether or not the algorithm interacted negatively with the spectral peaks (Equation ), and (c) quantify the signal‐to‐noise improvement (Equation ) relative to SNR of the original noisy spectrum ( R ( x i )).

{SNR}_{global} ((), r ((), x_{i})) = \frac{\max ((), r ((), x_{i}))}{italicRMSE ((),, r ((), x_{i}), S_{sig} ((), x_{i}))},

italicRMSE = \sqrt{\frac{\sum_{i = 1}^{N} {(r (x_{i}) - S_{italicsig} (x_{i}))}^{2}}{N},}

{SNR}_{peak} ((), r ((), x_{i})) = \frac{\max ((), r ((), x_{i}))}{italicRMSE ((),, r {(x_{i})}_{peak}, S_{sig} {(x_{i})}_{peak})},

{SNR}_{prod} ((), r ((), x_{i})) = \frac{{SNR}_{global} ((), r ((), x_{i}))}{{SNR}_{}}

…”

Section: Methodsmentioning

confidence: 99%

“…However, above certain noise levels, Gaussian noise is a good approximation for Poisson noise. [21,35] The sum of a mutually independent zero-mean Gaussian noise is still a zero-mean Gaussian noise with variance equal to the sum of the variances of the independent Gaussian noises. [36] Thus, spectroscopic noise can be modelled as the summation…”

Section: Samplesmentioning

confidence: 99%

“…of shot noise n ph (also referred to as photon noise), thermal noise n th , and readout noise n rd . [35,37] e(x i ) is Gaussian noise having a standard deviation of one and mean of zero. [36,38] The shot noise…”

Section: Samplesmentioning

confidence: 99%

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Vector casting for noise reduction

Gebrekidan

Knipfer

Braeuer

2020

J Raman Spectroscopy

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We report a new method for the reduction of noise from spectra. This method is based on casting vectors from one data point to the following data points of the noisy spectrum. The noise‐reduced spectrum is computed from the casted vectors within a margin that is identified by an envelope‐finder algorithm. We compared here the presented method with the Savitzky–Golay and the wavelet transform approaches for noise reduction using simulated Raman spectra of various signal‐to‐noise ratios between 1 and 25 dB and experimentally acquired Raman spectra. The method presented here performs well compared with the Savitzky–Golay and the wavelets‐based denoising method, especially at small signal‐to‐noise ratios and furthermore relies on a minimum of human input requirements.

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Section: Methodsmentioning

confidence: 99%

N_{sim} ((), x_{i}) = e ((), x_{i}) \sqrt{{n_{italicph}}^{2} ((), x_{i}) + {n_{italicth}}^{2} + {n_{italicrd}}^{2}}

of shot noise n ph (also referred to as photon noise), thermal noise n th , and readout noise n rd . e ( x i ) is Gaussian noise having a standard deviation of one and mean of zero .…”

Section: Methodsmentioning

confidence: 99%

{SNR}_{global} ((), r ((), x_{i})) = \frac{\max ((), r ((), x_{i}))}{italicRMSE ((),, r ((), x_{i}), S_{sig} ((), x_{i}))},

italicRMSE = \sqrt{\frac{\sum_{i = 1}^{N} {(r (x_{i}) - S_{italicsig} (x_{i}))}^{2}}{N},}

{SNR}_{peak} ((), r ((), x_{i})) = \frac{\max ((), r ((), x_{i}))}{italicRMSE ((),, r {(x_{i})}_{peak}, S_{sig} {(x_{i})}_{peak})},

{SNR}_{prod} ((), r ((), x_{i})) = \frac{{SNR}_{global} ((), r ((), x_{i}))}{{SNR}_{}}

…”

Section: Methodsmentioning

confidence: 99%

Section: Samplesmentioning

confidence: 99%

Section: Samplesmentioning

confidence: 99%

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Vector casting for noise reduction

Gebrekidan

Knipfer

Braeuer

2020

J Raman Spectroscopy

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Fundamentals and Applications of Raman‐Based Techniques for the Design and Development of Active Biomedical Materials

2023

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Raman spectroscopy is an analytical method based on light‐matter interactions that can interrogate the vibrational modes of matter and provide representative molecular fingerprints. Mediated by its label‐free, non‐invasive nature and high molecular specificity, Raman‐based techniques have become ubiquitous tools for in situ characterisation of materials. This review comprehensively describes the theoretical and practical background of Raman spectroscopy and its advanced variants. We highlight the numerous facets of material characterisation that Raman scattering can reveal, including biomolecular identification, solid‐to‐solid phase transitions and spatial mapping of biomolecular species in bioactive materials. The review illustrates the potential of these techniques in the context of active biomedical material design and development by highlighting representative studies from the literature. These studies cover the use of Raman spectroscopy for the characterisation of both natural and synthetic biomaterials, including engineered tissue constructs, biopolymer systems, ceramics and nanoparticle formulations, among others. To increase the accessibility and adoption of these techniques, the present review also provides the reader with practical recommendations on the integration of Raman techniques into the experimental laboratory toolbox. Finally, we provide perspectives on how recent developments in plasmon‐ and coherently‐enhanced Raman spectroscopy can propel Raman from underutilised to critical for biomaterial development.This article is protected by copyright. All rights reserved

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Enhancement of Signal‐to‐Background Ratio in Molecular Vibrational Signal Extraction by Stimulated Emission Depletion Mechanism

Wang,

Chen,

Zhan

et al. 2024

Advanced Photonics Research

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Herein, a novel approach is presented to mitigate the fluorescence interference during the detection of vibrational signal via the stimulated emission depletion (STED). STED is the mechanism commonly employed in optical imaging; however, its application should not be confined solely to this field. To explore additional possibilities, a novel application of STED in vibrational spectroscopy detection is introduced. Vibrational spectroscopy is a widely used technique for the material detection and identification, but its sensitivity is influenced by impurity signals, especially the fluorescence. The proposed method is capable of suppressing fluorescence without influencing vibrational signal. At the low concentration of fluorescent impurities, the signal‐to‐background ratio of vibrational spectroscopy is 2.6 times as high as that without this method. The introduction of depletion light can enhance the detection of vibrational signals, resulting in more optimal signal detection. A promising new application of STED other than super‐resolution imaging is investigated.

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Algorithm for optimal denoising of Raman spectra

Abstract: The algorithm enhances Savitzky–Golay smoothing with maximum likelihood estimation, which outperforms traditional smoothing in terms of peak fidelity and SNR.

Cited by 75 publications

References 19 publications

Vector casting for noise reduction

Vector casting for noise reduction

Fundamentals and Applications of Raman‐Based Techniques for the Design and Development of Active Biomedical Materials

Enhancement of Signal‐to‐Background Ratio in Molecular Vibrational Signal Extraction by Stimulated Emission Depletion Mechanism

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