Analysis of adaptive forward-backward diffusion flows with applications in image processing

V. B.Surya Prasath, Jos� Miguel Urbano, Dmitry Vorotnikov

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17 Scopus citations


The nonlinear diffusion model introduced by Perona and Malik (1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629-39) is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoizing results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.
Original languageEnglish (US)
JournalInverse Problems
Issue number10
StatePublished - Sep 24 2015
Externally publishedYes


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