arXiv subjects

Marcelo Cárdenas

Publications and source records attributed to Marcelo Cárdenas.

3 recordsLinked to original sources

arXiv2021

Multi-frame Super-resolution from Noisy Data

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).

cs.CV↗

arXiv2020

Stable Backward Diffusion Models that Minimise Convex Energies

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.

math.NA↗

arXiv2019

Existence Theory for the EED Inpainting Problem

We establish an existence theory for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at restoring missing data in an image as steady state of a nonlinear anisotropic diffusion process where the known data provide Dirichlet boundary conditions. We prove existence of a weak solution by applying the Leray-Schauder Fixed point theorem and show that the set of all possible weak solutions is bounded. Moreover, we demonstrate that under certain conditions, the sequences resulting from iterative application of the operator from the existence theory contain convergent subsequences.

math.AP↗