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

作者：Prasath V B Surya^*; Urbano Jose Miguel; Vorotnikov Dmitry

来源：Inverse Problems, 2015, 31(10): 105008.

DOI：10.1088/0266-5611/31/10/105008

• anisotropic diffusion
• regularization
• image restoration
• forward backward diffusion
• wellposedness
• total variation flow

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.

• 出版日期2015-10