Selective image-sharpness enhancement by coupled nonlinear reaction-diffusion time-evolution equations and its application to suppression of breathing distortions in moving pictures

2004 ◽  
Vol 87 (5) ◽  
pp. 33-47
Author(s):  
Takahiro Saito ◽  
Jun Satsumabayashi ◽  
Takashi Komatsu
Keyword(s):  
Time Evolution ◽  
Evolution Equations ◽  
Reaction Diffusion ◽  
Diffusion Time ◽  
Image Sharpness ◽  
Nonlinear Reaction ◽  
Sharpness Enhancement ◽  
Moving Pictures

Symmetries, ansätze and exact solutions of nonlinear second-order evolution equations with convection terms, II

2006 ◽  
Vol 17 (5) ◽  
pp. 597-605 ◽  
Author(s):  
ROMAN CHERNIHA ◽  
MYKOLA SEROV
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Second Order ◽  
Lie Symmetries ◽  
Nonlinear Reaction ◽  
Diffusion Convection ◽  
Natural Way

New results concerning Lie symmetries of nonlinear reaction-diffusion-convection equations, which supplement in a natural way the results published in the European Journal of Applied Mathematics (9(1998) 527–542) are presented.

Color image sharpening based on collective time-evolution of simultaneous nonlinear reaction-diffusion

2003 ◽  
Author(s):  
Takahiro Saito ◽  
Jun Satsumabayashi ◽  
Hiroyuki Harada ◽  
Takashi Komatsu
Keyword(s):  
Time Evolution ◽  
Color Image ◽  
Reaction Diffusion ◽  
Image Sharpening ◽  
Nonlinear Reaction

Numerical Resolution Near t = 0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1

2011 ◽  
Vol 9 (3) ◽  
pp. 568-586 ◽  
Author(s):  
Qingshan Chen ◽  
Zhen Qin ◽  
Roger Temam
Keyword(s):  
Evolution Equations ◽  
Space Dimension ◽  
Nonlinear Evolution ◽  
Reaction Diffusion ◽  
Nonlinear Evolution Equations ◽  
Reaction Diffusion Equation ◽  
Numerical Resolution ◽  
Nonlinear Reaction ◽  
Time Space ◽  
Nonlinear Reaction Diffusion Equation

AbstractThe incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner singularity issue for nonlinear evolution equations in 1D, and propose two remedy procedures that effectively recover much of the accuracy of the numerical scheme in use. Applications of the remedy procedures to the 1D viscous Burgers equation, and to the 1D nonlinear reaction-diffusion equation are presented. The remedy procedures are applicable to other nonlinear diffusion equations as well.

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