Some Forward-Backward and Nonlocal Diffusions of Image Processing

Patrick Guidotti
University of California, Irvine (UCI)

In this talk we shall discuss two types of nonlinear diffusions which have been proposed as mild regularizers for the well-known Perona-Malik equation (PME). One is nonlocal in nature and has the advantage to deliver a locally well-posed model (in the sense of classical solutions) without altering the dynamical behavior of PME solutions. The other is even milder in that it preserves the forward-backward feature of PME but admits global weak Young measure solutions the behavior of which is in complete agreement with numerical experiments. It also provides a suggestive explanation for the well-known staircasing phenomenon widely observed in numerical simulations of PME.

Presentation (PDF File)

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