Relative entropy maximization and directed diffusion equations

✍ Scribed by Reinhard Illner; Helmut Neunzert

• Book ID: 102514490
• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 421 KB
• Volume: 16
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670160803

✦ Synopsis

Abstract

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
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The relative entropy \documentclass{article}\pagestyle{empty}\begin{document}$ Sbf: = - \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.