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Image cryptosystems based on PottsNICA algorithms. Meng-Hong Chen Jiann-Ming Wu Department of Applied Mathematics National Donghwa University. Blind Source Separation (BSS). Sources. Unknown Mixing Structure. Observations. BSS by PottsICA. PottsNICA. Observations - PowerPoint PPT Presentation
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Image cryptosystems based on PottsNICA algorithms
Meng-Hong ChenJiann-Ming WuDepartment of Applied MathematicsNational Donghwa University
Blind Source Separation (BSS)
Sources
Observations
Unknown MixingStructure
BSS by PottsICA
Observations
Recovered sources
PottsNICA
The ICA problem
Unknown mixing structure:
Unkown statistical independent sources: S=
Observations:
The goal of ICA
The goal is to find W to recover independent sources by
The joint distribution is as close as possible to the product of the marginal distributions
such that
The criterion on independency of components of y can be quantified by he Kullback-Leibler divergence
The Kullback-Leibler Divergence
Then
The Kullback-Leibler Divergence
Partition the range of each output component
… …
Potts Modeling
Energy function for ICA
To minimize L’ is to solve a mixed integer and linear programming
Annealed neural dynamics
Boltzmann distribution
Use mean field equations to find the mean configuration at each
Derivation of mean field equations
Free energy by
Mean field equations
A hybrid of mean field annealing
MFE
( 1 )
( 2 )
Natural gradient descent method
W’W
W’W ( 3 )
The PottsNICA algorithm
SimulationsWe test the PottsICA method using facial images where the last one is a noise image. The parameters for the PottsICA algorithm are K=10, c₁=8, c₂=2 and η=0.001; the β parameter has an initial value of and each time it is increased to β by the scheduling process. The diagonal and last column of the mixing matrix A are lager than others. As follows,
Figure1
Original images
Mixtures of the sources by the mixing matrix A(4x4)
Recovered images by PossNICA
N = 4
Figure2
N = 5
Figure3
N = 8
Performance evaluations by Amari
Table
The performance of the three algorithms for tests by Amari evaluation
JadeICA FastICA PottsICA
K=10
PottsNICA
K=10
N=3 4.2921 6.5112 7.2942 1.5360
N=4 9.7240 11.8220 11.8763 3.3244
N=5 15.4743 15.1699 10.3392 4.8253
N=8 38.7841 35.3410 sigularity 19.2109