Section of Microtechnics, EPFL
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)