Parameter Identification of 1D Recurrent Fractal Interpolation Functions with Applications to Imaging and Signal Processing

Manousopoulos, Polychronis; Drakopoulos, Vasileios; Theoharis, Theoharis

doi:10.1007/s10851-010-0253-z

Cited by 16 publications

(6 citation statements)

References 14 publications

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“…Furthermore, we suppose that the idea of mapping on the basis of FJI can be extended to IFS as they are iterative. Consequently, the results of the present research can be applied to various applications associated with fractal interpolation functions such as signal processing and modeling coastlines and shapes [130,131,132,133,134].…”

Section: Discussionmentioning

confidence: 94%

Dynamics with Chaos and Fractals

Alejaily

Fen

Akhmet³

2020

Nonlinear Systems and Complexity

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, 98 pages In this thesis, we study how to construct and analyze dynamics for chaos and fractals. After the introductory chapter, we discuss in the second chapter the chaotic behavior of hydrosphere parameters and their influence on global weather and climate. For this purpose, we investigate the nature and source of unpredictability in the dynamics of sea surface temperature. The impact of sea surface temperature variability on the global climate is clear during some global climate patterns like the El Niño-Southern Oscillation. The interactions between these types of global climate patterns may transmit chaos. We discuss the unpredictability as a global phenomenon through extension of chaos horizontally and vertically by using theoretical as well as numerical analyses. In the third chapter, we introduce a technique concerning the construction of dynamics for fractals. Deterministic fractals like Julia sets are crucial for understanding the fractal phenomenon. These structures are deterministically arising from simple dynamics of iteration of analytic functions. On the basis of the dynamics, we develop a scheme to map fractals through iterations. This allows to involve fractals as states of dynamical systems as well as to introduce dynamics in fractals through differential and discrete equations. Creation of effective frameworks v for applications of fractals and assisting to explore the relationship between fractals and chaos by the involvement of dynamics in fractals are important aspects in this direction.

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Section: Discussionmentioning

confidence: 94%

Dynamics with Chaos and Fractals

Alejaily

Fen

Akhmet³

2020

Nonlinear Systems and Complexity

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“…For example, in [31] an analytic and a geometric method are proposed for minimising this squared error. In [32,33] the use of bounding volumes of data points subsets is proposed, to optimise the fit between original and transformed bounding volumes instead of individual points. Other methods use different approaches instead of minimising an error measure; in [34] the target is to preserve the fractal dimension of the data points; in [35] the target is to detect self-affinity and the implied vertical scaling factors in the continuous wavelet transform of the data.…”

Section: Self-affine Fractal Interpolation Functionsmentioning

confidence: 99%

Financial Time Series Modelling Using Fractal Interpolation Functions

Manousopoulos¹,

Drakopoulos

Polyzos

2023

AppliedMath

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Time series of financial data are both frequent and important in everyday practice. Numerous applications are based, for example, on time series of asset prices or market indices. In this article, the application of fractal interpolation functions in modelling financial time series is examined. Our motivation stems from the fact that financial time series often present fluctuations or abrupt changes which the fractal interpolants can inherently model. The results indicate that the use of fractal interpolation in financial applications is promising.

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“…Barnsley [33] introduced the idea of data interpolation using the fractal methodology of iterated function systems. Nowadays, fractal functions constitute a method of approximation of nondifferentiable mappings, providing suitable tools for the description of irregular signals (see [34][35][36][37][38][39]). The aim of this work is to prove common fixedpoint theorems for a pair of multivalued mappings in a b -metric space using H β -Hausdorff-Pompeiu b-metric and thereby extend and introduce new variants of various fixed-point results for multivalued mappings existing in literature.…”

Section: Introductionmentioning

confidence: 99%

$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

Alshammari

Alrashedi

George

2022

Journal of Function Spaces

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H β -Hausdorff functions for β ∈ 0 , 1 are introduced, and common fixed-point theorems for a pair of multivalued operators satisfying generalized contraction conditions are proven in a b -metric space. Our results are proper extensions and new variants of many contraction conditions existing in literature. In order to demonstrate applications of our result, we have proven an existence theorem for a unique common multivalued fractal of a pair of iterated multifunction systems and also an existence theorem for a common solution of a pair of Volterra-type integral equations.

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Parameter Identification of 1D Recurrent Fractal Interpolation Functions with Applications to Imaging and Signal Processing

Cited by 16 publications

References 14 publications

Dynamics with Chaos and Fractals

Dynamics with Chaos and Fractals

Financial Time Series Modelling Using Fractal Interpolation Functions

$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$

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Parameter Identification of 1D Recurrent Fractal Interpolation Functions with Applications to Imaging and Signal Processing

Cited by 16 publications

References 14 publications

Dynamics with Chaos and Fractals

Dynamics with Chaos and Fractals

Financial Time Series Modelling Using Fractal Interpolation Functions

H β -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a b

Contact Info

Product

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$H^{β}$ -Hausdorff Functions and Common Fixed Points of Multivalued Operators in a $b$