Electronic Resource
Chichester, West Sussex
:
Wiley-Blackwell
Mathematical Methods in the Applied Sciences
16 (1993), S. 545-554
ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy \documentclass{article}\pagestyle{empty}\begin{document}$ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $\end{document} is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i) - this is readily done because (i) has a large family of Ljapunov functionals.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670160803
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