Marcelo Cárdenas

Kireeti Bodduna, Joachim Weickert, Marcelo Cárdenas

Obtaining high resolution images from low resolution data with clipped noise is algorithmically challenging due to the ill-posed nature of the problem. So far such problems have hardly been tackled, and the few existing approaches use simplistic regularisers. We show the usefulness of two adaptive regularisers based on anisotropic diffusion ideas: Apart from evaluating the classical edge-enhancing anisotropic diffusion regulariser, we introduce a novel non-local one with one-sided differences and superior performance. It is termed sector diffusion. We combine it with all six variants of the classical super-resolution observational model that arise from permutations of its three operators for warping, blurring, and downsampling. Surprisingly, the evaluation in a practically relevant noisy scenario produces a different ranking than the one in the noise-free setting in our previous work (SSVM 2017).

Leif Bergerhoff, Marcelo Cárdenas, Joachim Weickert et al.

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a backward diffusion model which implements a smart stabilisation approach that can be used in combination with an easy to handle numerical scheme. So far, existing stabilisation strategies in literature require sophisticated numerics to solve the underlying initial value problem. We derive a class of space-discrete one-dimensional backward diffusion as gradient descent of energies where we gain stability by imposing range constraints. Interestingly, these energies are even convex. Furthermore, we establish a comprehensive theory for the time-continuous evolution and we show that stability carries over to a simple explicit time discretisation of our model. Finally, we confirm the stability and usefulness of our technique in experiments in which we enhance the contrast of digital greyscale and colour images.