The scaling properties of complex processes may be highly influenced by the presence of various artifacts in experimental recordings. Their removal produces changes in the singularity spectra and the Hölder exponents as compared with the original artifacts-free data, and these changes are significantly different for positively correlated and anti-correlated signals. While signals with power-law correlations are nearly insensitive to the loss of significant parts of data, the removal of fragments of anti-correlated signals is more crucial for further data analysis. In this work, we study the ability of characterizing scaling features of chaotic and stochastic processes with distinct correlation properties using a wavelet-based multifractal analysis, and discuss differences between the effect of missed data for synchronous and asynchronous oscillatory regimes. We show that even an extreme data loss allows characterizing physiological processes such as the cerebral blood flow dynamics.
References
1.
J.-F.
Muzy
, E.
Bacry
, and A.
Arneodo
, “Wavelets and multifractal formalism for singular signals: Application to turbulence data
,” Phys. Rev. Lett.
67
, 3515
–3518
(1991
).2.
J.-F.
Muzy
, E.
Bacry
, and A.
Arneodo
, “Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method
,” Phys. Rev. E
47
, 875
–884
(1993
).3.
J.-F.
Muzy
, E.
Bacry
, and A.
Arneodo
, “The multifractal formalism revisited with wavelets
,” Int. J. Bifurcation Chaos
4
, 245
–302
(1994
).4.
J. A.
Urigüen
and B.
Garcia-Zapirain
, “EEG artifact removal—state-of-the-art and guidelines
,” J. Neural Eng.
12
(3
), 031001
(2015
).5.
C.
Zhang
, L.
Tong
, Y.
Zeng
, J.
Jiang
, H.
Bu
, B.
Yan
, and J.
Li
, “Automatic artifact removal from electroencephalogram data based on a priori artifact information
,” BioMed Res. Intern.
2015
, 720450
(2015
).6.
N. P.
Castellanos
and V. A.
Makarov
, “Recovering EEG brain signals: Artifact suppression with wavelet enhanced independent component analysis
,” J. Neurosci. Methods
158
, 300
–312
(2006
).7.
Y.
Tran
, A.
Craig
, P.
Boord
, and D.
Craig
, “Using independent component analysis to remove artifact from electroencephalographic measured during stuttered speech
,” Med. Biol. Eng. Comput.
42
, 627
–633
(2004
).8.
E.
Urrestarazu
, J.
Iriarte
, M.
Alegre
, M.
Valencia
, C.
Viteri
, and J.
Artieda
, “Independent component analysis removing artifacts in ictal recordings
,” Epilepsia
45
, 1071
–1078
(2004
).9.
J. R.
Daube
and D. I.
Rubin
, Clinical Neurophysiology
(Oxford University Press
, New York
, 2009
).10.
Q. D. Y.
Ma
, R. P.
Bartsch
, P.
Bernaola-Galván
, M.
Yoneyama
, and P. Ch.
Ivanov
, “Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis
,” Phys. Rev. E
81
, 031101
(2010
).11.
C.-K.
Peng
, S. V.
Buldyrev
, S.
Havlin
, M.
Simons
, H. E.
Stanley
, and A. L.
Goldberger
, “Mosaic organization of DNA nucleotides
,” Phys. Rev. E
49
, 1685
–1689
(1994
).12.
C.-K.
Peng
, S.
Havlin
, H. E.
Stanley
, and A. L.
Goldberger
, “Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series
,” Chaos
5
, 82
–87
(1995
).13.
R. M.
Bryce
and K. B.
Sprague
, “Revisiting detrended fluctuation analysis
,” Sci. Rep.
2
, 315
(2012
).14.
U.
Frisch
and G.
Parisi
, “Fully developed turbulence and intermittency
,” in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics
, edited by M.
Ghil
, R.
Benzi
, and G.
Parisi
(North-Holland
, Amsterdam
, 1985
), pp. 71
–88
.15.
P. Ch.
Ivanov
, L. A.
Nunes Amaral
, A. L.
Goldberger
, S.
Havlin
, M. G.
Rosenblum
, Z. R.
Struzik
, and H. E.
Stanley
, “Multifractality in human heartbeat dynamics
,” Nature
399
, 461
–465
(1999
).16.
H. E.
Stanley
, L. A.
Nunes Amaral
, A. L.
Goldberger
, S.
Havlin
, P. C.
Ivanov
, and C.-K.
Peng
, “Statistical physics and physiology: Monofractal and multifractal approaches
,” Physica A
270
, 309
–324
(1999
).17.
A.
Arneodo
, N.
Decoster
, and S. G.
Roux
, “Intermittency, log-normal statistics, and multifractal cascade process in high-resolution satellite images of cloud structure
,” Phys. Rev. Lett.
83
, 1255
(1999
).18.
P.
Kestener
and A.
Arneodo
, “Three-dimensional wavelet-based multifractal method: The need for revisiting the multifractal description of turbulence dissipation data
,” Phys. Rev. Lett.
91
, 194501
(2003
).19.
J. W.
Kantelhardt
, S. A.
Zschiegner
, E.
Koscielny-Bunde
, S.
Havlin
, A.
Bunde
, and H. E.
Stanley
, “Multifractal detrended fluctuation analysis of nonstationary time series
,” Physica A
316
, 87
–114
(2002
).20.
P.
Oświȩcimka
, J.
Kwapień
, and S.
Drożdż
, “Wavelet versus detrended fluctuation analysis of multifractal structures
,” Phys. Rev. E
74
, 016103
(2006
).21.
J. S.
Murguía
and H. C.
Rosu
, “Multifractal analyses of row sum signals of elementary cellular automata
,” Physica A
391
(13
), 3638
–3649
(2012
).22.
J. S.
Murguía
, J. E.
Pérez-Terrazas
, and H. C.
Rosu
, “Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA
,” Europhys. Lett.
87
(2
), 28003
(2009
).23.
24.
I.
Daubechies
, Ten Lectures on Wavelets
(S.I.A.M
., Philadelphia
, 1992
).25.
A. N.
Pavlov
, A. S.
Abdurashitov
, O. A.
Sindeeva
, S. S.
Sindeev
, O. N.
Pavlova
, G. M.
Shihalov
, and O. V.
Semyachkina-Glushkovskaya
, “Characterizing cerebrovascular dynamics with the wavelet-based multifractal formalism
,” Physica A
442
, 149
–155
(2016
).26.
A. N.
Pavlov
, O. V.
Semyachkina-Glushkovskaya
, O. N.
Pavlova
, A. S.
Abdurashitov
, G. M.
Shihalov
, E. V.
Rybalova
, and S. S.
Sindeev
, “Multifractality in cerebrovascular dynamics: An approach for mechanisms-related analysis
,” Chaos, Solitons Fractals
91
, 210
–213
(2016
).27.
O. E.
Rössler
, “An equation for continuous chaos
,” Phys. Lett. A
57
, 397
–398
(1976
).28.
D. E.
Postnov
, T. E.
Vadivasova
, O. V.
Sosnovtseva
, A. G.
Balanov
, V. S.
Anishchenko
, and E.
Mosekilde
, “Role of multistability in the transition to chaotic phase synchronization
,” Chaos
9
, 227
–232
(1999
).29.
A. N.
Pavlov
, O. V.
Sosnovtseva
, and E.
Mosekilde
, “Scaling features of multimode motions in coupled chaotic oscillators
,” Chaos, Solitons Fractals
16
, 801
–810
(2003
).30.
L.
Minati
, M.
Frasca
, P.
Oświȩcimka
, L.
Faes
, and S.
Drożdż
, “Atypical transistor-based chaotic oscillators: Design, realization, and diversity
,” Chaos
27
, 073113
(2017
).31.
J. D.
Briers
and S.
Webster
, “Laser speckle contrast analysis (LASCA): A non-scanning, full-field technique for monitoring capillary blood flow
,” J. Biomed. Opt.
1
, 174
–179
(1996
).32.
D. A.
Boas
and A. K.
Dunn
, “Laser speckle contrast imaging in biomedical optics
,” J. Biomed. Opt.
15
, 011109
(2010
).33.
S.
Liu
, P.
Li
, and Q.
Luo
, “Fast blood flow visualization of high-resolution laser speckle imaging data using graphics processing unit
,” Opt. Express
16
, 14321
(2008
).34.
A. N.
Pavlov
, O. V.
Semyachkina-Glushkovskaya
, V. V.
Lychagov
, A. S.
Abdurashitov
, O. N.
Pavlova
, O. A.
Sindeeva
, and S. S.
Sindeev
, “Multifractal characterization of cerebrovascular dynamics in newborn rats
,” Chaos, Solitons Fractals
77
, 6
–10
(2015
).© 2018 Author(s).
2018
Author(s)
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