Microcanonical multifractal formalism—a geometrical approach to multifractal systems: Part I. Singularity analysis

Turiel, Antonio; Yahia, Hussein; Pérez-Vicente, Conrad J.

doi:10.1088/1751-8113/41/1/015501

Cited by 83 publications

(200 citation statements)

References 63 publications

Supporting

Mentioning

189

Contrasting

Unclassified

Order By: Relevance

“…(1) can be applied we will prefer to speak about Hölder exponents. Assessment based on Hölder exponents can only be applied to very specific signals; in general, the presence of long range correlations and the effects of noise and discretization would preclude a direct evaluation of the scaling exponent [27,32].…”

Section: Definition Of Singularity Analysismentioning

confidence: 99%

“…(7), even positive functions [32]. As discussed in [29], the resolution capability of a wavelet depends on the number of zero-crossings it has, which is increased in higher-order wavelets but is minimum for positive wavelets.…”

Section: Definition Of Singularity Analysismentioning

confidence: 99%

“…In [30] a new question was posed: if the hierarchy truly exists in complex signals, can they be reconstructed starting from the vertex of this hierarchy? For multifractals, the set associated to the vertex is well-known, at least from the theoretical point of view: it is the so-called Most Singular Component (MSC), which is the set comprising the points with most singular (i.e., most negative) values of h(x) [27,32].…”

Section: Msc and Its Connection With Reconstructionmentioning

confidence: 99%

“…This new approach to singularity analysis is in the basis of the so-called Microcanonical Multiscale Formalism (MMF) [32], which has been shown to be useful to assess physical properties of turbulent flows and other multiscale systems [24,6,31,32,28,15,17,16]. It has been hence demonstrated that obtaining the singularity exponents at each point of a signal can reveal many useful information not only about the image, but also about the physical processes giving raise to it.…”

Section: Introductionmentioning

confidence: 99%

“…However, the performance of MMF-based singularity analysis (namely, the quality of the exponents calculated with this approach) depends on the properties of the multiscaling function used [32], the best multiscaling functions being positive functions with fast enough decay [21]. Although for statistical analysis almost any scaling function gives the same results [29], a precise geometrical determination of the underlying patterns, edges and textures requires a very fine tuning of the multiscaling function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals

Pont

Turiel

Yahia

2011

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Section: Definition Of Singularity Analysismentioning

confidence: 99%

Section: Definition Of Singularity Analysismentioning

confidence: 99%

Section: Msc and Its Connection With Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals

Pont

Turiel

Yahia

2011

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Detecting the surface salinity signature of Gulf Stream cold‐core rings in Aquarius synergistic products

et al. 2015

View full text Add to dashboard Cite

New sea surface salinity (SSS) observations derived from satellite remote sensing platforms provide a comprehensive view of salt exchanges across boundary currents such as the Gulf Stream. The high resolution (45 km spatial resolution and 3 day repeat subcycle) of the Soil Moisture and Ocean Salinity (SMOS) observations allows detection (and tracking) of meander and ring structures of the Gulf Stream from SSS maps. These structures are, however, not resolved by the relatively lower resolution (100 km and 7 day repeat subcycle) of Aquarius observations. A recently developed fusion technique, based on singularity analysis, is applied in this study to reconstruct these mesoscale (from 100 km and 3 days) features in Aquarius-derived products. New quarter-degree SSS maps are obtained by fusing Aquarius data with three different geophysical templates: sea surface height (SSH) from AVISO, SSS from SMOS, and sea surface temperature (SST) from AVHRR. The proposed method exploits the theoretical correspondence among the singularity exponents of different maps of ocean-surface remotely sensed scalar fields. The analysis results over the year 2012 show that merging Aquarius with SSH data provides a series of negative salinity anomalies that better collocate with the position of the cyclonic eddies identified from sea level anomaly maps. This result is consistent with the hypothesis that this SLA derived cyclonic eddies in this area are indeed CCRs shed off the GS.

show abstract

ASCAT wind quality under high subcell wind variability conditions

et al. 2015

View full text Add to dashboard Cite

The assessment and validation of the quality of satellite scatterometer vector winds is challenging under increased subcell wind variability conditions, since reference wind sources such as buoy winds or model output represent very different spatial scales from those resolved by scatterometers (i.e., increased representativeness error). In this paper, moored buoy wind time series are used to assess the correlation between subcell wind variability and several Advanced Scatterometer (ASCAT)‐derived parameters, such as the wind‐inversion residual, the backscatter measurement variability factor, and the singularity exponents derived from an image processing technique, called singularity analysis. It is proven that all three ASCAT parameters are sensitive to the subcell wind variability and complementary in flagging the most variable winds, which is useful for further application. A triple collocation (TC) analysis of ASCAT, buoy, and the European Centre for Medium‐range Weather Forecasting (ECMWF) model output is then performed to assess the quality of each wind data source under different variability conditions. A novel approach is used to compute the representativeness errors, a key ingredient for the TC analysis. The experimental results show that the estimated errors of each wind source increase as the subcell wind variability increases. When temporally averaged buoy winds are used instead of 10 min buoy winds, the TC analysis results in smaller buoy wind errors (notably at increased wind variability conditions) while ASCAT and ECMWF errors do not significantly change, further validating the proposed TC approach. It is concluded that at 25 km resolution, ASCAT provides the best quality winds in general.

show abstract

Microcanonical multifractal formalism—a geometrical approach to multifractal systems: Part I. Singularity analysis

Cited by 83 publications

References 63 publications

An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals

An Optimized Algorithm for the Evaluation of Local Singularity Exponents in Digital Signals

Detecting the surface salinity signature of Gulf Stream cold‐core rings in Aquarius synergistic products

ASCAT wind quality under high subcell wind variability conditions

Contact Info

Product

Resources

About