Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion

Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information of where the image is corrupted, and others that do it. While the first algorithm is able to reconstruct only images that our visual system is...

The Differentiation of Hypoelliptic Diffusion Semigroups

Basic derivative formulas are presented for hypoelliptic heat semi-groups and harmonic functions extending earlier work in the elliptic case. Following the approach of 15], emphasis is placed on developing integration by parts formulas at the level of local martingales. Combined with the optional sampling theorem, this turns out to be an eecient way of dealing with boundary conditions, as well ...

Image Restoration via Nonstandard Diffusion

We present a functional of nonstandard growth for which the corresponding minimization problem provides a model for image denoising, enhancement, and restoration. The diffusion resulting from the proposed model is a combination of isotropic and anisotropic diffusion. Isotropic diffusion is used at locations with low gradient and total variation based diffusion is used along likely edges. At all...

Holistic Image Reconstruction for Diffusion MRI

Diffusion MRI provides unique information on the microarchitecture of biological tissues. One of the major challenges is finding a balance between image resolution, acquisition duration, noise level and image artifacts. Recent methods tackle this challenge by performing super-resolution reconstruction in image space or in diffusion space, regularization of the image data or of postprocessed dat...

Image Reconstruction from Incomplete Data