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Synthesis of bidimensional α-stable models withlong-range dependence

xiaodong sunMESA (Mechatronics, Embedded Systems and Automation)Lab

School of Engineering,University of California, Merced

E: xsun7@ucmerced.edu Phone:209 201 1947Lab: CAS Eng 820 (T: 228-4398)

sep 22, 2014. Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

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The paper we talk about

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

Beatrice Pesquet-Popescu a, ∗, Jean-Christophe Pesquetb

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Why need 2D fractal modelThe 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 α-stable models

Generate multivariate stable distribution noise

Generate long-range dependence (LRD) behaviors

bidimensional α-stable models with long-range dependence

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Generate multivariate α-stable driving noise According to the proposition 1.7.1 in paper [1]. The α-stable driving

noise can be generated[1]G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes:

Stochastic Models with Infinite Variance, Chapman and Hall, New York, 1994.

MESA LabGenerate 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

MESA LabGenerate long-range dependence α-stable processes

Generate 2D α-stable processes X

Apply FFT to X ,W=fft(X)

α-stable noise pass 2D filter Hd() . Generate S=W.Hd()

α-stable process with LRD by using inverse . Ss=ifft2(S)

MESA LabSimulation

pcolor α=1.4 d=0.25

MESA LabSimulation

contour3 α=1.4 d=0.25

MESA LabSimulation

pcolor α=1.6 d=0.3

MESA LabSimulation

contour3 α=1.6 d=0.3

MESA LabSimulation

pcolor α=1.8 d=0.35

MESA LabSimulation

contour3 α=1.8 d=0.35

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Thank you !