ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm

Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such features is the utilization of parabolic scaling. One prominent example is the shearlet system. Our objective in this paper is three-fold: We firstly develop a digital shearlet theory which is rationally designed in the sense that it is the digitization of the existing shearlet theory for continuous data. This implicates that shearlet theory provides a unified treatment of both the continuum and digital realm. Secondly, we analyze the utilization of pseudo-polar grids and the pseudo-polar Fourier transform for digital implementations of parabolic scaling algorithms. We derive an isometric pseudo-polar Fourier transform by careful weighting of the pseudo-polar grid, allowing exploitation of its adjoint for the inverse transform. This leads to a digital implementation of the shearlet transform; an accompanying Matlab toolbox called ShearLab is provided. And, thirdly, we introduce various quantitative measures for digital parabolic scaling algorithms in general, allowing one to tune parameters and objectively improve the implementation as well as compare different directional transform implementations. The usefulness of such measures is exemplarily demonstrated for the digital shearlet transform.Comment: submitted to SIAM J. Multiscale Model. Simu

Weighted Repeated Median Smoothing and Filtering

We propose weighted repeated median filters and smoothers for robust non-parametric regression in general and for robust signal extraction from time series in particular. The proposed methods allow to remove outlying sequences and to preserve discontinuities (shifts) in the underlying regression function (the signal) in the presence of local linear trends. Suitable weighting of the observations according to their distances in the design space reduces the bias arising from non-linearities. It also allows to improve the efficiency of (unweighted) repeated median filters using larger bandwidths, keeping their properties for distinguishing between outlier sequences and long-term shifts. Robust smoothers based on weighted L1- regression are included for the reason of comparison. --Signal extraction ; Robust regression ; Outliers ; Breakdown point

Final Report of the DAUFIN project

DAUFIN = Data Assimulation within Unifying Framework for Improved river basiN modeling (EC 5th framework Project

Life-cycle assessment of buildings: a Review

Life-Cycle Assessment (LCA) is one of various management tools for evaluating environmental concerns. This paper reviews LCA from a buildings perspective. It highlights the need for its use within the building sector, and the importance of LCA as a decision making support tool. It discusses LCA methodologies and applications within the building sector, reviewing some of the life-cycle studies applied to buildings or building materials and component combinations within the last fifteen years in Europe and the United States. It highlights the problems of a lack of an internationally comparable and agreed data inventory and assessment methodology which hinder the application of LCA within the building industry. It identifies key areas for future research as (i) the whole process of construction, (ii) the relative weighting of different environmental impacts and (iii) applications in developing countries