Image inpainting with second-order diffusion

Philippe Favre

Semester Project

Section of Microtechnics, EPFL

July 2012

Abstract

During this semester project, new methods for image restoration were studied. Many imaging problems can be expressed as the solution of a linear inverse problem. One approach for solving this kind of problems is to use a variational method. The minimization of a regularizer under the consistency constraint can lead to a diffusion partial differential equation (PDE).
First-order regularizers, such as the Total Variation (TV) regularization, have already been studied in the literature. A first-order diffusion PDE is related to the minimization of the TV regularizer. It is possible to see that the modification of the diffusivity term in the first-order PDE can lead to improvements in terms of image restoration quality.
A recent paper showed that a second-order Hessian-based regularization method, leading to second-order diffusion PDE, gives better restoration than the first-order diffusion restoration. The motivation is now to modify the diffusivity term in the second-order diffusion PDE to explore if it can lead to even better restoration results.
This thesis is mainly focused on restoring a randomly masked image. The figure below shows the result of restoration from 2% of observed samples of Lena. (Left: Original image. Center: Observed image, 2% of Lena. Right: Second-order diffusion based restoration)