scholarly journals WAVELET-BASED MULTIFRACTAL FORMALISM TO ASSIST IN DIAGNOSIS IN DIGITIZED MAMMOGRAMS

2011 ◽  
Vol 20 (3) ◽  
pp. 169 ◽  
Author(s):  
Pierre Kestener ◽  
Jean Marc Lina ◽  
Philippe Saint-Jean ◽  
Alain Arneodo
Keyword(s):  
Wavelet Transform ◽  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Computer Assisted ◽  
Scaling Properties ◽  
Multifractal Formalism ◽  
Long Range Correlations ◽  
Multifractal Scaling ◽  
Self Similar ◽  
Assisted Diagnosis

We apply the 2D wavelet transform (WTMM) method to perform a multifractal analysis of digitized mammograms. We show that normal regions display monofractal scaling properties as characterized by the socalled Hurst exponent H =0.3±0.1 in fatty areas which look like antipersistent self-similar random surfaces, while H=0.65±0.1 in dense areas which exibit long-range correlations and possibly multifractal scaling properties. We further demonstrate that the 2D WTMM method provides a very efficient way to detect tumors as well as microcalcifications (MC) which correspond to much stronger singularities than those involved in the background tissue roughness fluctuations. These preliminary results indicate that the texture discriminatory power of the 2D WTMM method may lead to significant improvement in computer-assisted diagnosis in digitized mammograms.

Cardiac Arrhythmia Detection using Dual Tree Wavelet Transform and Convolutional Neural Network

2021 ◽  
Author(s):  
K Reddy Madhavi ◽  
Padmavathi kora ◽  
L Venkateswara Reddy ◽  
J Avanija ◽  
KLS Soujanya ◽  
...  
Keyword(s):  
Neural Network ◽  
Wavelet Transform ◽  
Cardiac Cells ◽  
P Wave ◽  
Computer Assisted ◽  
Ecg Signals ◽  
Coronary Diseases ◽  
Life Saving ◽  
Life Threatening ◽  
Assisted Diagnosis

Abstract The non-stationary ECG signals are used as a key tools in screening coronary diseases. ECG recording is collected from millions of cardiac cells’ and depolarization and re-polarization conducted in a synchronized manner as: The P-wave occurs first, followed by the QRScomplex and the T-wave, which will repeat in each beat. The signal is altered in a cardiac beat period for different heart conditions. This change can be observed in order to diagnose the patient’s heart status. There are life-threatening (critical) and non-life - threatening (noncritical) arrhythmia (abnormal Heart). Critical arrhythmia gives little time for surgery, whereas non-critical needs additional life-saving care. Simple naked eye diagnosis can mislead the detection. At that point, Computer Assisted Diagnosis (CAD) is therefore required. In this paper Dual Tree Wavelet Transform (DTWT) used as a feature extraction technique along with Convolution Neural Network (CNN) to detect abnormal Heart. The findings of this research and associated studies are without any cumbersome artificial environments. The CAD method proposed has high generalizability; it can help doctors efficiently identify diseases and decrease misdiagnosis.

Conditional and Relative Multifractal Spectra

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 153-168 ◽  
Author(s):  
Rudolf H. Riedi ◽  
Istvan Scheuring
Keyword(s):  
Multifractal Analysis ◽  
Mutual Influence ◽  
Multifractal Spectrum ◽  
Real Data ◽  
The Novel ◽  
Multifractal Formalism ◽  
Geometrical Properties ◽  
Single Mechanism ◽  
Novel Approach ◽  
Self Similar

In the study of the involved geometry of singular distributions, the use of fractal and multifractal analysis has shown results of outstanding significance. So far, the investigation has focussed on structures produced by one single mechanism which were analyzed with respect to the ordinary metric or volume. Most prominent examples include self-similar measures and attractors of dynamical systems. In certain cases, the multifractal spectrum is known explicitly, providing a characterization in terms of the geometrical properties of the singularities of a distribution. Unfortunately, strikingly different measures may possess identical spectra. To overcome this drawback we propose two novel methods, the conditional and the relativemultifractal spectrum, which allow for a direct comparison of two distributions. These notions measure the extent to which the singularities of two distributions 'correlate'. Being based on multifractal concepts, however, they go beyond calculating correlations. As a particularly useful tool, we develop the multifractal formalism and establish some basic properties of the new notions. With the simple example of Binomial multifractals, we demonstrate how in the novel approach a distribution mimics a metric different from the usual one. Finally, the applications to real data show how to interpret the spectra in terms of mutual influence of dense and sparse parts of the distributions.

LOCAL SCALING PROPERTIES OF FRACTALS OBSERVED IN Ni-Zr ALLOY FILMS

1990 ◽  
Vol 04 (17) ◽  
pp. 1111-1118 ◽  
Author(s):  
J.R. DING ◽  
F. WANG ◽  
B.X. LIU
Keyword(s):  
Wavelet Transform ◽  
Mass Distribution ◽  
Multifractal Analysis ◽  
Ion Irradiation ◽  
Potential Gradient ◽  
Alloy Films ◽  
Scaling Properties ◽  
Local Scaling ◽  
Wide Range ◽  
Zr Alloy

Wavelet transform was performed based on the fractals observed in Ni-Zr alloy films during ion irradiation. The mass distribution measure and the Laplacian potential gradient measure were used to study the local scaling properties of the ion-induced fractals. The strength of singularities at each point was calculated according to the wavelet transform. The densities of the strength of singularities were also deduced and compared with the f-α spectra yielded by multifractal analysis. The results showed that the ion-induced fractals had a wide range of strength of singularities.

A WAVELET MULTIFRACTAL FORMALISM FOR SIMULTANEOUS SINGULARITIES OF FUNCTIONS

2013 ◽  
Vol 12 (01) ◽  
pp. 1450009 ◽  
Author(s):  
JAMIL AOUIDI ◽  
ANOUAR BEN MABROUK
Keyword(s):  
Multifractal Analysis ◽  
Multifractal Formalism ◽  
Self Similar

In this paper, a wavelet multifractal analysis is developed which permits to characterize simultaneous singularities for a vector of functions. An associated multifractal formalism is introduced and checked for the case of functions involving self similar aspects.

scholarly journals Multifractal Analysis of SARS-CoV-2 Coronavirus genomes using the wavelet transform

2020 ◽  
Author(s):  
Sid-Ali Ouadfeul
Keyword(s):  
Wavelet Transform ◽  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Genome Structure ◽  
The Self ◽  
Self Organization ◽  
Dna Coding ◽  
Wavelet Transform Modulus Maxima ◽  
Range Correlation ◽  
Modulus Maxima

AbstractIn this paper, the 1D Wavelet Transform Modulus Maxima lines (WTMM) method is used to investigate the Long-Range Correlation (LRC) and to estimate the so-called Hurst exponent of 21 isolate RNA sequence downloaded from the NCBI database of patients infected by SARS-CoV-2, Coronavirus, the Knucleotidic, Purine, Pyramidine, Ameno, Keto and GC DNA coding are used. Obtained results show the LRC character in the most sequences; except some sequences where the anti-correlated or the Classical Brownian motion character is observed, demonstrating that the SARS-Cov2 coronavirus undergoes mutation from a country to another or in the same country, they reveals also the complexity and the heterogeneous genome structure organization far from the equilibrium and the self-organization.

scholarly journals DETERMINING LOCAL SINGULARITY STRENGTHS AND THEIR SPECTRA WITH THE WAVELET TRANSFORM

Fractals ◽  
2000 ◽  
Vol 08 (02) ◽  
pp. 163-179 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Multifractal Analysis ◽  
Real Life ◽  
Life Time ◽  
Hölder Exponent ◽  
Multifractal Formalism ◽  
Wavelet Transform Modulus Maxima ◽  
Local Singularity ◽  
Modulus Maxima ◽  
Multiplicative Cascade

We present a robust method of estimating the effective strength of singularities (the effective Hölder exponent) locally at an arbitrary resolution. The method is motivated by the multiplicative cascade paradigm, and implemented on the hierarchy of singularities revealed with the wavelet transform modulus maxima (WTMM) tree. In addition, we illustrate the direct estimation of the scaling spectrum of the effective singularity strength, and we link it to the established partition function-based multifractal formalism. We motivate both the local and the global multifractal analysis by showing examples of computer-generated and real-life time series.

scholarly journals Identification of Fractal Properties in Geomagnetic Data of Southeast Asian Region during Various Solar Activity Levels

Universe ◽  
2021 ◽  
Vol 7 (7) ◽  
pp. 248
Author(s):  
Farhan Naufal Rifqi ◽  
Nurul Shazana Abdul Hamid ◽  
A. Babatunde Rabiu ◽  
Akimasa Yoshikawa
Keyword(s):  
Solar Activity ◽  
Hurst Exponent ◽  
Equatorial Region ◽  
Activity Levels ◽  
Scaling Properties ◽  
Fractal Properties ◽  
Spectral Peaks ◽  
Multifractal Scaling ◽  
Quiet Day

The fractal properties of geomagnetic northward component data (H-component) in the equatorial region during various phases of solar activity over Southeast Asia were investigated and then quantified using the parameter of the Hurst exponent (H). This study began with the identification of existence of spectral peaks and scaling properties in international quiet day H-component data which were measured during three levels of solar activity: low, intermediate, and high. Then, various cases of quiet and disturbed days during different solar activity levels were analyzed using the method that performed the best in the preceding part. In all the years analyzed, multifractal scaling and spectral peaks exist, signifying that the data have fractal properties and that there are external factors driving the fluctuations of geomagnetic activity other than solar activity. The analysis of various cases of quiet and disturbed days generally showed that quiet days had anti-persistence tendencies (H < 0.5) while disturbed days had persistence tendencies (H > 0.5)—generally a higher level of Hurst exponent compared to quiet days. As for long-term quiet day H-component data, it had a Hurst exponent value that was near H ≃ 0.50, while the long-term disturbed day H-component data showed higher values than that of the quiet day.

MULTIFRACTAL ANALYSIS OF SOME WEIGHTED QUASI-SELF-SIMILAR FUNCTIONS

2011 ◽  
Vol 09 (06) ◽  
pp. 965-987 ◽  
Author(s):  
JAMIL AOUIDI ◽  
ANOUAR BEN MABROUK
Keyword(s):  
Finite Number ◽  
Multifractal Analysis ◽  
Similar Case ◽  
Gibbs Measures ◽  
Box Dimension ◽  
Multifractal Formalism ◽  
Spectrum Of Singularities ◽  
Self Similar

In this paper, a multifractal analysis of some non-self-similar functions based on the superposition of finite number of weighted quasi-self-similar ones ∑iωiFi is developed. In general, such superpositions do not yield neither a self-similar nor a quasi-self-similar outcome. Furthermore, there are two main problems that appear. Firstly, a phenomenon of regularity compensation may exist. Secondly, the computation of the spectrum of singularities and therefore the validity of the multifractal formalism based on the possibility of constructing Gibbs measures fail. In this paper, we propose to study such problems by conducting a multifractal analysis of such combinations and to check the validity of the multifractal formalism in the case where there is no compensation of regularity. Furthermore, we compute the box dimension of the associated graphs and provide some examples. The paper in its full subject re-considers the results of Ref. 3 in the quasi-self-similar case.

scholarly journals A MIXED MULTIFRACTAL ANALYSIS FOR QUASI-AHLFORS VECTOR-VALUED MEASURES

Fractals ◽  
2021 ◽  
pp. 2240001
Author(s):  
ANOUAR BEN MABROUK ◽  
ADEL FARHAT
Keyword(s):  
Large Class ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Probability Measures ◽  
Original Formulation ◽  
Multifractal Formalism ◽  
Self Similar ◽  
Joint Multifractal Analysis ◽  
Vector Valued ◽  
Special Classes

The multifractal formalism for measures in its original formulation is checked for special classes of measures, such as, doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to prove the validity of the multifractal formalism. In this work, a large class of measures satisfying a weak condition known as quasi-Ahlfors is considered in the framework of mixed multifractal analysis. A joint multifractal analysis of finitely many quasi-Ahlfors probability measures is developed. Mixed variants of multifractal generalizations of Hausdorff, and packing measures, and corresponding dimensions are introduced. By applying convexity arguments, some properties of these measures, and dimensions are established. Finally, an associated multifractal formalism is introduced, and proved to hold for the class of quasi-Ahlfors measures. Besides, some eventual applications, and motivations, especially, in AI are discussed.

scholarly journals Aggregation-and-Attention Network for brain tumor segmentation

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Chih-Wei Lin ◽  
Yu Hong ◽  
Jinfu Liu
Keyword(s):  
Brain Tumor ◽  
Semantic Information ◽  
Spatial Relationship ◽  
Tumor Segmentation ◽  
Computer Assisted ◽  
Brain Tumor Segmentation ◽  
Attention Network ◽  
Multi Scale ◽  
Assisted Diagnosis ◽  
The Brain

Abstract Background Glioma is a malignant brain tumor; its location is complex and is difficult to remove surgically. To diagnosis the brain tumor, doctors can precisely diagnose and localize the disease using medical images. However, the computer-assisted diagnosis for the brain tumor diagnosis is still the problem because the rough segmentation of the brain tumor makes the internal grade of the tumor incorrect. Methods In this paper, we proposed an Aggregation-and-Attention Network for brain tumor segmentation. The proposed network takes the U-Net as the backbone, aggregates multi-scale semantic information, and focuses on crucial information to perform brain tumor segmentation. To this end, we proposed an enhanced down-sampling module and Up-Sampling Layer to compensate for the information loss. The multi-scale connection module is to construct the multi-receptive semantic fusion between encoder and decoder. Furthermore, we designed a dual-attention fusion module that can extract and enhance the spatial relationship of magnetic resonance imaging and applied the strategy of deep supervision in different parts of the proposed network. Results Experimental results show that the performance of the proposed framework is the best on the BraTS2020 dataset, compared with the-state-of-art networks. The performance of the proposed framework surpasses all the comparison networks, and its average accuracies of the four indexes are 0.860, 0.885, 0.932, and 1.2325, respectively. Conclusions The framework and modules of the proposed framework are scientific and practical, which can extract and aggregate useful semantic information and enhance the ability of glioma segmentation.

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