Synthesis of bidimensional a-stable models with long-range dependence

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Synthesis of bidimensional a-stable models
withlong-range dependence

• xiaodong sun
• MESA (Mechatronics, Embedded Systems and
  Automation)Lab
• School of Engineering,
• University of California, Merced
• E xsun7_at_ucmerced.edu Phone[phone]
• Lab CAS Eng 820 (T 228-4398)

sep 22, 2014. Applied Fractional Calculus
Workshop Series _at_ MESA Lab _at_ UCMerced
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The paper we talk about

• Synthesis of bidimensional a-stable models with
  long-range dependence
• Beatrice Pesquet-Popescu a, ,
  Jean-Christophe Pesquetb

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Why need 2D fractal model

• The motivation for modeling and synthesizing
  textures with impulsive and long-range dependence
  (LRD) behaviors are on the following
• Segmentation of synthetic or satellite images(
  high-speckle SAR imagery )
• ultrasound medical imaging and astronomical
  imaging.
• In computer graphic applications, the generation
  of 2-D picture realizations( create
  natural-looking night landscapes)
• Underwater image modeling (Scattering effect
  caused by water molecule)
• Camera internal noise modeling

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The way to bidimensional a-stable models
Generate multivariate stable distribution noise
Generate long-range dependence (LRD) behaviors
bidimensional a-stable models with long-range
dependence
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Generate multivariate a-stable driving noise

• According to the proposition 1.7.1 in paper 1.
  The a-stable driving noise can be generated
• 1G. Samorodnitsky, M.S. Taqqu, Stable
  Non-Gaussian Random Processes Stochastic Models
  with Infinite Variance, Chapman and Hall, New
  York, 1994.

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Generate long-range dependence (LRD) behaviors
'fractionally differenced' processes are
capable of modelling long-term persistence. 2D
discrete-space process with LRD properties can be
achieved by a 2D fractional stable process
passed a bidimensional filter system . the
frequency response of the bidimensional filter
can be expressed by
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Generate long-range dependence a-stable processes

Generate 2D a-stable processes X
Apply FFT to X ,Wfft(X)
a-stable noise pass 2D filter Hd() . Generate
SW.Hd()
a-stable process with LRD by using inverse .
Ssifft2(S)
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Simulation pcolor a1.4 d0.25
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Simulation contour3 a1.4 d0.25
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Simulation pcolor a1.6 d0.3
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Simulation contour3 a1.6 d0.3
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Simulation pcolor a1.8 d0.35
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Simulation contour3 a1.8 d0.35
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• Thank you !