Filtration and Restoration of Satellite Images Using Doubly Stochastic Random Fields
Transcript of Filtration and Restoration of Satellite Images Using Doubly Stochastic Random Fields
FILTRATION AND RESTORATION OF SATELLITE IMAGES USING DOUBLY STOCHASTIC RANDOM FIELDS
Professor, Doctor of Engineering Konstantin Vasiliev,
PhD, Assistant ProfessorVitaliy Dementiev,and PhD Student Nikita Andriyanov
Ulyanovsk State Technical (Russia)
RELEVANCE
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PROBLEM
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SOLUTIONS
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IMAGE RESTORATION
FILTERING
???MODELLING
SINGULAR VALUE DECOMPOSITION OF MATRICES WITH GAPS
KOHONEN MAPS
GOAL AND TASKS
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.
DOUBLY STOCHASTIC MODEL
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Consider the following modification of a doubly stochastic model
where is the random field of correlation parameters by the row; is the random field of correlation parameters by the column; is the random field of independent Gaussian random values with and ; is the base random field dispersion.
ijjiijijjiijjiijij xxxx 11211211 ,,,
ij1 ij2 ij
0 mM ij
))(( 22
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222 11 ijijxijijM 2x
IMAGES FITTING
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a) b) c)
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PARAMETERS ESTIMATION USING SLIDING WINDOW
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EXAMPLES OF IMAGE RESTORATION
Restoration of the area of the image on the border of two dissimilar surfaces
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EXAMPLES OF IMAGE RESTORATION
Restoration of the image area close to uniform
EXAMPLES OF IMAGE RESTORATION
Restoration of the image area limited by different structures
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RESTORATION DURING FILTRATION
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We carry out a similar study, when to estimate the parameters of a doubly stochastic model we use the Kalman filter. To filter flat images we will use vector (interline) nonlinear Kalman filter. To do this, combine the elements of the image into a vector line . Then the model image can be written as
TiNiii xxxx ,,, 21
iyixiixii xdiagx ,)( 1 xixixxxi r )1(1 yiyiyyyi r )1(1
xiN
xi
xi
xidiag
0......
...0
......0...0...
0...
)( 2
1
In this progressive evaluation process can be described by the known nonlinear Kalman filter equations:
эpiinpi
T
iэpipi xzVx
Pxx ˆˆˆ 1
PSEUDOGRADIENT SEARCH
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)ˆ,((ˆˆ 1111 tttttt ZJ
Pseudogradient estimation procedure will be carried out in accordance with the following general expression
where is vector of parameters to estimate; t is an iteration number; is the approximation matrix; is the pseudogradient of objective function J, that characterizes the quality of estimation; Zt is the local sample of observations using at t-th iteration.
1111111111 2khgfedcba
xzij )ˆ(min}~{
2222222222 2khgfedcba
xzij )ˆ(min}~{
Thus, we select the coefficients by minimizing each of the possible directions of joint changes
PSEUDOGRADIENT AGAINST SLIDING WINDOW
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THE RESTORATION
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CONCLUSION- we have synthesized image reconstruction algorithms based on models with a complex structure;-we have obtained the gain in comparison with the AR models (from 1.5 to 6 times depending on the image type);-we have suggested combine using of the pseudogradient search procedures and Kalman filter for image restoration;-processing of various images has been investigated. Doubly stochastic models provides gain to 5 times compared with the AR models.
THANK YOU FOR YOUR ATTENTION!
Nikita Andriyanov,Ulyanovsk State Technical University (Russia)
email: [email protected]