We will attempt to solve an Image Denoising Problem [1] by using modifications of the heat equation. In particular, we will explore regularity and capabilites of Perona-Malik [2] diffusion and introduce a complex diffusion coefficient to obtain an ramp preserving improvement [3] of the PM diffusion while still maintaing the second-order degree of the PDE.

 

Reference:

[1] Aubert, Gilles, and Pierre Kornprobst. Mathematical problems in image processing: partial differential equations and the calculus of variations. Vol. 147. Springer Science & Business Media, 2006.

[2] Perona, Pietro, and Jitendra Malik. "Scale-space and edge detection using anisotropic diffusion." IEEE Transactions on pattern analysis and machine intelligence 12.7 (1990): 629-639.

[3] Gilboa, Guy, Nir Sochen, and Yehoshua Y. Zeevi. "Image enhancement and denoising by complex diffusion processes." IEEE transactions on pattern analysis and machine intelligence 26.8 (2004): 1020-1036.

 

Meeting Room link will be announced at 14:00, May. 5.