9,225 research outputs found
Discretization schemes and numerical approximations of PDE impainting models and a comparative evaluation on novel real world MRI reconstruction applications
While various PDE models are in discussion since the last ten years and are widely applied nowadays in image processing and computer vision tasks, including restoration, filtering, segmentation and object tracking, the perspective adopted in the majority of the relevant reports is the view of applied mathematician, attempting to prove the existence theorems and devise exact numerical methods for solving them. Unfortunately, such solutions are exact for the continuous PDEs but due to the discrete approximations involved in image processing, the results yielded might be quite unsatisfactory. The major contribution of This work is, therefore, to present, from an engineering perspective, the application of PDE models in image processing analysis, from the algorithmic point of view, the discretization and numerical approximation schemes used for solving them. It is of course impossible to tackle all PDE models applied in image processing in this report from the computational point of view. It is, therefore, focused on image impainting PDE models, that is on PDEs, including anisotropic diffusion PDEs, higher order non-linear PDEs, variational PDEs and other constrained/regularized and unconstrained models, applied to image interpolation/ reconstruction. Apart from this novel computational critical overview and presentation of the PDE image impainting models numerical analysis, the second major contribution of This work is to evaluate, especially the anisotropic diffusion PDEs, in novel real world image impainting applications related to MRI
Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets
In some models of quantum gravity, space-time is thought to have a foamy
structure with non-trivial optical properties. We probe the possibility that
photons propagating in vacuum may exhibit a non-trivial refractive index, by
analyzing the times of flight of radiation from gamma-ray bursters (GRBs) with
known redshifts. We use a wavelet shrinkage procedure for noise removal and a
wavelet `zoom' technique to define with high accuracy the timings of sharp
transitions in GRB light curves, thereby optimizing the sensitivity of
experimental probes of any energy dependence of the velocity of light. We apply
these wavelet techniques to 64 ms and TTE data from BATSE, and also to OSSE
data. A search for time lags between sharp transients in GRB light curves in
different energy bands yields the lower limit GeV on
the quantum-gravity scale in any model with a linear dependence of the velocity
of light . We also present a limit on any quadratic dependence.Comment: This version is accepted for publication in Astronomy & Astrophysics.
The discussion and introduction are extended making clear why the wavelet
analysis should be superior to straight cross-correlation analysis. More
details on compiled data are elaborated. 18 pages, 9 figures, A&A forma
- …