We propose and analyze a symmetric weighted interior penalty (SWIP) method to approximate in a Discontinuous Galerkin framework advection-diffusion equations with anisotropic and discontinuous diffusivity. The originality of the method consists in the use of diffusivity-dependent weighted averages to better cope with locally small diffusivity (or equivalently with locally high Péclet numbers) o...

SENSE (SENSitivity Encoding) imaging provides significant acquisition speedups in MRI. The main drawback of the method is that it generates images that have increased and spatially nonuniform noise levels and, hence, will often require retrospective filtering. In this paper, we show that standard anisotropic diffusion filtering, while being an effective technique for edgepreserving denoising of...

To enlarge a digital image from a single frame preserving the perceptive cues is a relevant research issue. The best known algorithms take into account the presence of edges in the luminance channel, to interpolate correctly the samples/pixels of the original image. This approach allows the production of pictures where the interpolated artifacts (aliasing blurring effect,...) are limited but wh...

A novel nonlinear PDE based image denoising and restoration approach is provided in this article. The proposed anisotropic diffusion based technique is derived from the influential Perona-Malik nonlinear diffusion scheme, representing an enhanced version of that scheme. Our model is based on new versions of the edge-stopping function and the conductance parameter. The proposed PDE-based filteri...

2 Magnetic and optical properties of liquid crystalline colloidal particles 33 2. Introduction This work is concerned with the solution of an important problem of influence of a magnetic field on rotational diffusion in anisotropic colloidal solutions. It describes the results of experimental investigations of the author carried out using the method of diffusing-wave spectroscopy and the method...

Image restoration has been an active research area. Different formulations are effective in high quality recovery. Partial Differential Equations (PDEs) have become an important tool in image processing and analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kind of anisotropic diffusion (ANDI) filter. Anisotropic diffusion filter has become a valuable tool in dif...

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, contro...

Tensor-driven anisotropic diffusion and regularisation have been successfully applied to a wide range of image processing and computer vision tasks such as denoising, inpainting, and optical flow. Empirically it has been shown that anisotropic models with a diffusion tensor perform better than their isotropic counterparts with a scalar-valued diffusivity function. However, the reason for this s...

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, contro...

A novel approach to the detection of multiple sclerosis (MS) lesions is presented, which uses an adaptive formulation of the anisotropic diffusion and fuzzy-c-means (FCM) clustering. As opposite to previous works of the same authors, FCM runs only on PD weighted slices that, for each examination, are composed in a unique data set. Images are preprocessed with an anisotropic diffusion filter who...