Abstract

Brillouin spectroscopy can suffer from low signal-to-noise ratios (SNRs). Such low SNRs can render common data analysis protocols unreliable, especially for SNRs below ∼10. In this work we exploit two denoising algorithms, namely maximum entropy reconstruction (MER) and wavelet analysis (WA), to improve the accuracy and precision in determination of Brillouin shifts and linewidth. Algorithm performance is quantified using Monte-Carlo simulations and benchmarked against the Cramér-Rao lower bound. Superior estimation results are demonstrated even at low SNRs (≥ 1). Denoising is furthermore applied to experimental Brillouin spectra of distilled water at room temperature, allowing the speed of sound in water to be extracted. Experimental and theoretical values were found to be consistent to within ±1% at unity SNR.

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2019 (2)

P. Török and M. R. Foreman, “Precision and informational limits in inelastic optical spectroscopy,” Sci. Rep. 9(1), 6140 (2019).
[Crossref]

R. Prevedel, A. Diz-Mu noz, G. Ruocco, and G. Antonacci, “Brillouin microscopy - a revolutionary tool for mechanobiology?” Nat. Methods 16(10), 969–977 (2019).
[Crossref]

2018 (5)

E. Edrei and G. Scarcelli, “Brillouin micro-spectroscopy through aberrations via sensorless adaptive optics,” Appl. Phys. Lett. 112(16), 163701 (2018).
[Crossref]

S. Mattana, M. Mattarelli, L. Urbanelli, K. Sagini, C. Emiliani, M. D. Serra, D. Fioretto, and S. Caponi, “Non-contact mechanical and chemical analysis of single living cells by microspectroscopic techniques,” Light: Sci. Appl. 7(2), 17139 (2018).
[Crossref]

Z. Coker, M. Troyanova-Wood, A. J. Traverso, T. Yakupov, Z. N. Utegulov, and V. V. Yakovlev, “Assessing performance of modern Brillouin spectrometers,” Opt. Express 26(3), 2400–2409 (2018).
[Crossref]

D. Akilbekova, V. Ogay, T. Yakupov, M. Sarsenova, B. Umbayev, A. Nurakhmetov, K. Tazhin, V. V. Yakovlev, and Z. N. Utegulov, “Brillouin spectroscopy and radiography for assessment of viscoelastic and regenerative properties of mammalian bones,” J. Biomed. Opt. 23(9), 1–11 (2018).
[Crossref]

S. Colabrese, M. Castello, G. Vicidomini, and A. Del Bue, “Machine learning approach for single molecule localisation microscopy,” Biomed. Opt. Express 9(4), 1680–1691 (2018).
[Crossref]

2017 (2)

I. V. Kabakova, Y. Xiang, C. Paterson, and P. Török, “Fiber-integrated Brillouin microspectroscopy: Towards Brillouin endoscopy,” J. Innovative Opt. Health Sci. 10(06), 1742002 (2017).
[Crossref]

A. Karampatzakis, C. Z. Song, L. P. Allsopp, A. Filloux, S. A. Rice, Y. Cohen, T. Wohland, and P. Török, “Probing the internal micromechanical properties of Pseudomonas aeruginosa biofilms by Brillouin imaging,” npj Biofilms Microbiomes 3(1), 20 (2017).
[Crossref]

2016 (6)

M. Tsang, R. Nair, and X. M. Lu, “Quantum theory of superresolution for two incoherent optical point sources,” Phys. Rev. X 6(3), 031033 (2016).
[Crossref]

Z. Meng, A. J. Traverso, C. W. Ballmann, M. A. Troyanova-Wood, and V. V. Yakovlev, “Seeing cells in a new light: a renaissance of Brillouin spectroscopy,” Adv. Opt. Photonics 8(2), 300–327 (2016).
[Crossref]

C. W. Ballmann, J. V. Thompson, A. J. Traverso, Z. Meng, M. O. Scully, and V. V. Yakovlev, “Stimulated Brillouin Scattering Microscopic Imaging.,” Sci. Rep. 5(1), 18139 (2016).
[Crossref]

G. Lepert, R. M. Gouveia, C. J. Connon, and C. Paterson, “Assessing corneal biomechanics with Brillouin spectro-microscopy,” Faraday Discuss. 187, 415–428 (2016).
[Crossref]

X. Li, T. Yang, S. Li, D. Wang, Y. Song, and S. Zhang, “Raman spectroscopy combined with principal component analysis and k nearest neighbour analysis for non-invasive detection of colon cancer,” Laser Phys. 26(3), 035702 (2016).
[Crossref]

M. Srivastava, C. L. Anderson, and J. H. Freed, “A New Wavelet Denoising Method for Selecting Decomposition Levels and Noise Thresholds,” IEEE Access 4, 3862–3877 (2016).
[Crossref]

2015 (4)

G. Scarcelli, W. J. Polacheck, H. T. Nia, K. Patel, A. J. Grodzinsky, R. D. Kamm, and S. H. Yun, “Noncontact three-dimensional mapping of intracellular hydromechanical properties by Brillouin microscopy,” Nat. Methods 12(12), 1132–1134 (2015).
[Crossref]

G. Scarcelli, S. Besner, R. Pineda, P. Kalout, and S. H. Yun, “In Vivo Biomechanical Mapping of Normal and Keratoconus Corneas,” JAMA Ophthalmol. 133(4), 480–482 (2015).
[Crossref]

G. Antonacci, R. M. Pedrigi, A. Kondiboyina, V. V. Mehta, R. de Silva, C. Paterson, R. Krams, and P. Török, “Quantification of plaque stiffness by Brillouin microscopy in experimental thin cap fibroatheroma,” J. R. Soc., Interface 12(112), 20150843 (2015).
[Crossref]

G. Antonacci, G. Lepert, C. Paterson, and P. Török, “Elastic suppression in Brillouin imaging by destructive interference,” Appl. Phys. Lett. 107(6), 061102 (2015).
[Crossref]

2014 (3)

S. Speziale, H. Marquardt, and T. S. Duffy, “Brillouin Scattering and its Application in Geosciences,” Rev. Mineral. Geochem. 78(1), 543–603 (2014).
[Crossref]

A. Small and S. Stahlheber, “Fluorophore localization algorithms for super-resolution microscopy,” Nat. Methods 11(3), 267–279 (2014).
[Crossref]

A. R. Small and R. Parthasarathy, “Superresolution localization methods,” Annu. Rev. Phys. Chem. 65(1), 107–125 (2014).
[Crossref]

2012 (1)

P. Lasch, “Spectral pre-processing for biomedical vibrational spectroscopy and microspectroscopic imaging,” Chemom. Intell. Lab. Syst. 117, 100–114 (2012).
[Crossref]

2010 (1)

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7(5), 373–375 (2010).
[Crossref]

2008 (2)

2006 (4)

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[Crossref]

S. T. Hess, T. P. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91(11), 4258–4272 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

S. Ram, E. S. Ward, and R. J. Ober, “Beyond Rayleigh’s criterion: A resolution measure with application to single-molecule microscopy,” Proc. Natl. Acad. Sci. U. S. A. 103(12), 4457–4462 (2006).
[Crossref]

2005 (1)

K. J. Koski and J. L. Yarger, “Brillouin imaging,” Appl. Phys. Lett. 87(6), 061903 (2005).
[Crossref]

2004 (1)

R. J. Ober, S. Ram, and E. S. Ward, “Localization Accuracy in Single-Molecule Microscopy,” Biophys. J. 86(2), 1185–1200 (2004).
[Crossref]

2003 (1)

2002 (1)

D. Liu, J. Xu, R. Li, R. Dai, and W. Gong, “Measurements of sound speed in the water by Brillouin scattering using pulsed Nd:YAG laser,” Opt. Commun. 203(3-6), 335–340 (2002).
[Crossref]

1998 (1)

K.-B. Li, A. S. Stern, and J. C. Hoch, “Distributed Parallel Processing for Multidimensional Maximum Entropy Reconstruction,” J. Magn. Reson. 134(1), 161–163 (1998).
[Crossref]

1996 (1)

1995 (2)

D. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41(3), 613–627 (1995).
[Crossref]

D. L. Donoho and I. M. Johnstone, “Adapting to Unknown Smoothness via Wavelet Shrinkage,” J. Am. Stat. Assoc. 90(432), 1200–1224 (1995).
[Crossref]

1992 (1)

N. Bonnet, E. Simova, S. Lebonvallet, and H. Kaplan, “New applications of multivariate statistical analysis in spectroscopy and microscopy,” Ultramicroscopy 40(1), 1–11 (1992).
[Crossref]

1988 (1)

J. Barzilai and J. M. Borwein, “Two-Point Step Size Gradient Methods,” IMA J. Numer. Anal. 8(1), 141–148 (1988).
[Crossref]

1986 (1)

S. A. Lee, D. A. Pinnick, S. M. Lindsay, and R. C. Hanson, “Elastic and photoelastic anisotropy of solid HF at high pressure,” Phys. Rev. B 34(4), 2799–2806 (1986).
[Crossref]

1984 (2)

S. Kawata and S. Minami, “Adaptive Smoothing of Spectroscopic Data by a Linear Mean-Square Estimation,” Appl. Spectrosc. 38(1), 49–58 (1984).
[Crossref]

J. Skilling and R. Bryan, “Maximum entropy image reconstruction: general algorithm,” Mon. Not. R. Astron. Soc. 211(1), 111–124 (1984).
[Crossref]

1982 (1)

J. G. Ables, “Maximum Entropy Spectral Analysis,” Astro. Astrophys. Supp. 15, 383–393 (1982).

1978 (1)

S. F. Gull and G. J. Daniell, “Image reconstruction from incomplete and noisy data,” Nature 272(5655), 686–690 (1978).
[Crossref]

1971 (1)

P. Wolfe, “Convergence Conditions for Ascent Methods. II: Some Corrections,” SIAM Rev. 13(2), 185–188 (1971).
[Crossref]

1964 (1)

A. Savitzky and M. J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Anal. Chem. 36(8), 1627–1639 (1964).
[Crossref]

Ables, J. G.

J. G. Ables, “Maximum Entropy Spectral Analysis,” Astro. Astrophys. Supp. 15, 383–393 (1982).

Akilbekova, D.

D. Akilbekova, V. Ogay, T. Yakupov, M. Sarsenova, B. Umbayev, A. Nurakhmetov, K. Tazhin, V. V. Yakovlev, and Z. N. Utegulov, “Brillouin spectroscopy and radiography for assessment of viscoelastic and regenerative properties of mammalian bones,” J. Biomed. Opt. 23(9), 1–11 (2018).
[Crossref]

Allsopp, L. P.

A. Karampatzakis, C. Z. Song, L. P. Allsopp, A. Filloux, S. A. Rice, Y. Cohen, T. Wohland, and P. Török, “Probing the internal micromechanical properties of Pseudomonas aeruginosa biofilms by Brillouin imaging,” npj Biofilms Microbiomes 3(1), 20 (2017).
[Crossref]

Anastasio, M. A.

M. A. Anastasio and R. W. Schoonover, “Basic Principles of Inverse Problems for Optical Scientists,” in The Optics Encyclopedia, 1–24, (Wiley-VCH Verlag GmbH & Co., 2016).

Anderson, C. L.

M. Srivastava, C. L. Anderson, and J. H. Freed, “A New Wavelet Denoising Method for Selecting Decomposition Levels and Noise Thresholds,” IEEE Access 4, 3862–3877 (2016).
[Crossref]

Antonacci, G.

R. Prevedel, A. Diz-Mu noz, G. Ruocco, and G. Antonacci, “Brillouin microscopy - a revolutionary tool for mechanobiology?” Nat. Methods 16(10), 969–977 (2019).
[Crossref]

G. Antonacci, G. Lepert, C. Paterson, and P. Török, “Elastic suppression in Brillouin imaging by destructive interference,” Appl. Phys. Lett. 107(6), 061102 (2015).
[Crossref]

G. Antonacci, R. M. Pedrigi, A. Kondiboyina, V. V. Mehta, R. de Silva, C. Paterson, R. Krams, and P. Török, “Quantification of plaque stiffness by Brillouin microscopy in experimental thin cap fibroatheroma,” J. R. Soc., Interface 12(112), 20150843 (2015).
[Crossref]

Ballmann, C. W.

Z. Meng, A. J. Traverso, C. W. Ballmann, M. A. Troyanova-Wood, and V. V. Yakovlev, “Seeing cells in a new light: a renaissance of Brillouin spectroscopy,” Adv. Opt. Photonics 8(2), 300–327 (2016).
[Crossref]

C. W. Ballmann, J. V. Thompson, A. J. Traverso, Z. Meng, M. O. Scully, and V. V. Yakovlev, “Stimulated Brillouin Scattering Microscopic Imaging.,” Sci. Rep. 5(1), 18139 (2016).
[Crossref]

Barzilai, J.

J. Barzilai and J. M. Borwein, “Two-Point Step Size Gradient Methods,” IMA J. Numer. Anal. 8(1), 141–148 (1988).
[Crossref]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[Crossref]

Berglund, A. J.

Besner, S.

G. Scarcelli, S. Besner, R. Pineda, P. Kalout, and S. H. Yun, “In Vivo Biomechanical Mapping of Normal and Keratoconus Corneas,” JAMA Ophthalmol. 133(4), 480–482 (2015).
[Crossref]

Betzig, E.

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Figures (3)

Fig. 1.
Fig. 1. Bias of estimates of the Brillouin shift found by Lorentzian fitting of simulated noisy spectral data subject to different denoising algorithms, as calculated using 5000 realisations of simulated noise.
Fig. 2.
Fig. 2. Logarithm of the standard deviation of estimates of the Brillouin shift, found by Lorentzian fitting of simulated noisy spectral data subject to different denoising algorithms, as calculated using 5000 realisations of simulated noise.
Fig. 3.
Fig. 3. Example of a typical unprocessed experimental Brillouin spectrum of distilled water obtained using a 100 ms acquisition time ($\mbox {SNR}\sim 5$) (blue). Corresponding reconstructed spectra as found using the WA (orange) and MER (yellow) algorithms are also shown. Note that spectra have been vertically shifted to improve visibility.

Tables (1)

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Table 1. Speed of sound in distilled water as obtained from Lorentzian fitting of experimental Brillouin spectra subject to the MER and WA algorithms as compared to no pre-processing.

Equations (10)

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S = i = 1 N f i log f i
d i = j = 1 N R i j f j
χ 2 = 1 N i , j = 1 N ( R i j f j d j ) 2 σ j 2 ,
Q = S λ ( χ 2 χ 0 2 )
f n + 1 = f n + μ P
max { Q ( f ) | f R + n } .
d i = j = 1 N R i j f j + n i
d ~ = DWT [ d ] = g ~ + n ~
Universal threshold Q = n 2 ln ( N ) / N
σ Ω 2 π Δ 4 X 2 ( α Γ ± + γ ) 3 SNR 2 ( 1 + 2 I ± ) 2 α 2 I ± 2 .