MESA Lab
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: [email protected] Phone:209 201 1947Lab: CAS Eng 820 (T: 228-4398)
sep 22, 2014. Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced
MESA Lab
The paper we talk about
Synthesis of bidimensional α-stable models with long-range dependence
Beatrice Pesquet-Popescu a, ∗, Jean-Christophe Pesquetb
MESA Lab
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
MESA Lab
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
MESA Lab
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)