in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

The linear and nonlinear scale spaces are generalized in the complex domain, by combining the di usion equation with the simpli ed Schr odinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex di usion shows that the generalized di usion has properties of both forward and inverse di usion. An important observation, supported theoretically a...

the purpose of this letter is to revisit the nonlinear reaction-diusion modelin porous catalysts when reaction term is fractional function of the concen-tration distribution of the reactant. this model, which originates also in uidand solute transport in soft tissues and microvessels, has been recently givenanalytical solution in terms of taylors series for dierent family of reactionterms. we...

A framework that naturally uni es smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the di usion equation with the simpli ed schrodinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex di usion shows that the generalized di usion has properties of both ...

We present two nonlinear di usion processes with timedependent di usion coeÆcients. Both processes converge to nontrivial solutions, eliminating the need to impose an arbitrary di usion stopping time, otherwise required in the implementation of most nonlinear diffusion processes. The two schemes employ nonlinear cooling mechanisms that preserve edges. One scheme is intended for general denoisin...

Scale-space representation has been extensively studied in the computer vision community for analyzing image structures at di erent scales. This paper borrows and develops useful mathematical tools from scale-space theory to facilitate the task of image compression. Instead of compressing the original image directly, we propose to compress its scale-space representation obtained by the forward ...

A novel local scale controlled piecewise linear di usion for selective smoothing and edge detection is presented. The di usion stops at the place and time determined by the minimum reliable local scale and a spatial variant, anisotropic local noise estimate. It shows nisotropic, nonlinear di usion equation using di usion coe cients/tensors that continuously depend on the gradient is not necessa...

A novel local scale controlled piecewise linear diffusion for selective smoothing and edge detection is presented. The di usion stops at the place and time determined by the minimum reliable local scale and a spatial variant, anisotropic local noise estimate. It shows nisotropic, nonlinear di usion equation using di usion coe cients/tensors that continuously depend on the gradient is not necess...

Operator splitting methods are often used to solve convection di usion prob lems of convection dominated nature However it is well known that such methods can produce signi cant splitting errors in regions containing self sharpening fronts To amend this shortcoming corrected operator splitting methods have been developed These ap proaches use the wave structure from the convection step to ident...

We derive a two-scale homogenization limit for reaction-di usion systems where for some species the di usion length is of order 1 whereas for the other species the di usion length is of the order of the periodic microstructure. Thus, in the limit the latter species will display di usion only on the microscale but not on the macroscale. Because of this missing compactness, the nonlinear coupling...