AG Numerik

## Software

Here you can find a collection of our local software (mostly Matlab programs). They are freely distributed under the test GNU General Public License. Please be sure to read the GPL before downloading any software tool!

The following software packages may be downloaded:

• Wavelet and Multiscale Library (C++) -> website
The Wavelet and Multiscale Library is a collection of adaptive wavelet algorithms for partial differential equations, complemented by some additional wavelet tools.

• Villemoes Machine (Matlab) -> download (-> documentation)
The Villemoes Machine is to estimate a lower bound for the Sobolev regularity of refinable functions using the Villemoes trick.
(See "L. Villemoes, Wavelet analysis of refinement equations, SIAM J. Math. Anal. 25 (1994), 1433-1460")

• Multiwavelet Assistant (Matlab) -> download
With the Multiwavelet Assistant, you can compute the critical Sobolev exponent of a given scaling vector and create plots of scaling vectors and the corresponding multiwavelets.
(See "R. Q. Jia and Q. T. Jiang, Spectral analysis of the transition operator and its applications to smoothness analysis of wavelets, SIAM J. Matrix Anal. Appl. 24 (2003), 1071-1109")

• Multitiling Plotter (Matlab) -> download
With the Multitiling Plotter, you can easily visualize multitilings, using the algorithm from [GHR].
(See "K.-H. Gröchenig, A. Haas, and A. Raugi, Self-affine tilings with several tiles I, Applied and Computational Harmonic Analysis 7 (1999), 211-238")

• Image Processing: (An)isotrop diffusion filtering of images (Java GUI, C++ program) -> download
This software package contains an implementation of specific denoising algorithms as developed by Joachim Weickert. The algorithm provides a method to denoise an image without destroying important features such as edges. The idea is to use the image as an initial value for a parabolic differential equation. Then, the smoothing properties of parabolic equations give rise to denoising. To preserve edges, nonlinear diffusion is used, that is, in regions with strong gradients (edges) the diffusivity is attenuated. Several diffusion functions are implemented. Diffusion may take place in regions of the picture with low local differences (isotropic). An advanced feature is the anisotropic diffusion. Here a local gradient is considered and diffusion in this and the orthogal direction may be specified. This allows denoising also in areas with high gradients.
Download includes: executables (Linux/Mac/Windows), documentation of the tool, report about usage of different diffusion functions, report about choice of parameters (all documentation in german language)
(See "J. Weickert, Anisotropic Diffusion in Image Proecessing", Teubner, Stuttgart, 1998"
"J. Weickert, "Applications of nonlinear diffusion in image processing and computer vision, Acta Math. Univ. Comenianae 70 (200), 33-50."
"T. Brox, Von Pixeln zu Regionen: Partielle Differentialgleichungen in der Bildanalyse, dissertation, Saarländische Universitäts- und Landesbibliothek (2005)"
"T. Künzel, Nichtlineare Diffusion: Theoretische Analyse und Anwendungen bei Strömungssimulationen, diploma thesis, Philipps-Universtity Marburg (2007)")

• Adaptive Spline Approximation (C++ & Matlab) -> download (-> documentation)
This software package displays adaptive approximation of functions using stepwise or linear functions.