Multidimensional Models for Methodological Validation in Multifractal Analysis

Lopes, Renaud; Dubois, Patrick; Bhouri, Imen; Puech, Philippe; Maouche, S.; Betrouni, Nacim

doi:10.1109/iembs.2007.4353602

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Different properties have been established by simulation when the true process is a fractional Brownian process [29], and ARFIMA(p,d,q) processes [30], even in the presence of trends. However, the length of the series considered on these papers are short enough to generate doubts about the estimation accuracy of α, when working with real data.…”

Section: Propertiesmentioning

confidence: 99%

Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Kembro,

Flesia,

Gleiser

et al. 2013

Preprint

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The aim of this study was to evaluate the performance of a classical method of fractal analysis, Detrended Fluctuation Analysis (DFA), in the analysis of the dynamics of animal behavior time series. In order to correctly use DFA to assess the presence of long-range correlation, previous authors using statistical model systems have stated that different aspects should be taken into account such as: 1) the establishment by hypothesis testing of the absence of short term correlation, 2) an accurate estimation of a straight line in the log-log plot of the fluctuation function, 3) the elimination of artificial crossovers in the fluctuation function, and 4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus). In our study, modeling the data with the general ARFIMA model, we rejected the hypothesis of short range correlations (d=0) in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail, and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations.

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Section: Propertiesmentioning

confidence: 99%

Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Kembro,

Flesia,

Gleiser

et al. 2013

Preprint

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Classification of brain SPECT imaging using 3D local multifractal spectrum for epilepsy detection

Lopes

Dubois²,

Makni

et al. 2008

Int J CARS

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Purpose Multifractal spectrum analysis is a discriminating tool that may distinguish volunteers and epileptic patients. In this study, our aim was to detect epileptogenic sources by computing the singularity spectrum. Materials and methods Multifractal analysis based on generalized concepts of fractals has been applied to evaluate biological tissues composed of complex structures. This analysis can provide a precise quantitative description for a broad range of heterogeneous phenomena. This study investigates the possibility of using a mathematical model (multifractal analysis) for image texture to detect the underlying source changes on SPECT images. Previously, reported on application of 3D multifractal analysis to describe the multifractal character of brain SPECT (Single-Photon Emission Computed Tomography) images and we showed that the multifractal spectrum is a discriminating tool to distinguish volunteers and epileptic patients. The experiment is divided into two phases. First, we developed a 3D method for the singularity spectrum compute. In the test phase, we applied this multifractal spectrum to the detection of epileptogenic sources in SPECT images. ResultsThe results obtained on a group of seven patients show that the proposed method is feasible and the results are encouraging. The epileptic fit sources obtained using the R. Lopes (B) · P. Dubois · N. Makni · N. Betrouni INSERM, U703, ITM, Pavillon Vancostenobel, system were in agreement with the opinion of expert diagnosticians. Conclusion Multifractal spectrum analysis provides a means of detecting and localizing epileptogenic foci in brain SPECT scans.

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3D mutifractal analysis: A new tool for epileptic fit sources detection in SPECT images

Lopes

Viard

Dewalle

et al. 2008

2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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One of the imaging modalities used for the diagnosis of epilepsy is SPECT (Single-Photon Emission Computed Tomography). Ictal and interictal images are registered to MR images (SISCOM (Substracted Ictal Spect COregistred to MR) to delineate the sources. However, in some cases and for many reasons, the used method does not lead to precise delimitation of epileptic fit sources. In this case, works have been investigated on group's studies or in combining others modalities like EEG (Electroencephalography). This study investigates the possibility of using a mathematic model for the image texture to detect the changes on SPECT images. Beyond encouraging preliminary results concerning the multifractal analysis to distinguish volunteers and epileptic patients, our aim was to detect sources by the singularity spectrum compute. The experiment is divided into two phases. First, we developed a 3D method for the singularity spectrum compute. In the test phase, we applied this multifractal spectrum to the sources detection on SPECT images. The results obtained on a base of seven patients show that the proposed method is encouraging. Indeed, the detections of epileptic fit sources obtained were in agree with the expert diagnostic.

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Multidimensional Models for Methodological Validation in Multifractal Analysis

Abstract: Abstract. Multifractal analysis is known as a useful tool in signal analysis. However, the methods are often used without methodological validation. In this study, we present multidimensional models in order to validate multifractal analysis methods.

Cited by 4 publications

References 17 publications

Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Classification of brain SPECT imaging using 3D local multifractal spectrum for epilepsy detection

3D mutifractal analysis: A new tool for epileptic fit sources detection in SPECT images

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