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

Gender, Social Capital and Collective Action: A gender perspective on collective sustainability of water resource governance in west Nepal

In Nepal, as in other South Asian countries, water resource development is often considered to be a primarily technological challenge, requiring engineered solutions. Many years of advocacy for gender equality in water management - drawing attention to the need for local institutional changes has shifted this outlook. Thus, today women’s participation in water user associations (WUA) is encouraged and identified to be key in enabling gender equality, a more equal participation in water governance, and a more equal share of water infrastructure and services. Nonetheless, these well intention efforts tend to overlook complex social dynamics in rural areas, which influence the effectiveness of women’s participation. If initiatives to engaging women are to succeed in promoting gender equality, they must be considered in the light of the wider social and political contexts – of what makes for a community, a society

Controlling root flies with exclusion fences?

Protecting crops with insect fences is currently being considered as an alternative to row cover netting and synthetic insecticides. Previous studies reported efficacies of such fences with 50-90 % reduction in crop damage by root flies. We conducted trials with a 1.70 m fence over two years to monitor carrot rust fly (Psila rosae) in carrots and cabbage root fly (Delia radicum) in radish. There was a significant reduction in cabbage root fly damage in fenced plots whereas no such effect could be found with carrot rust fly. The structure of the overhang at the top of the fence and the mobility of this particular species may be important elements to consider in fence design. The length of the overhang also seemed to be important for cabbage root fly (Delia radicum) control, as a statistically significant treatment effect was observed only when the overhang was 35 cm long. Using radish as a test crop, the fences reduced damage by 55 % in the second year of the trial. The population size of overwintering cabbage root flies was also an important factor, as the number of flies in the year that the fence was effective was lower than in the previous year

Asymptotic Analysis of Inpainting via Universal Shearlet Systems

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional representation systems have often been utilized. One prominent example of this class are shearlets, which have the additional benefitallowing faithful implementations. Numerical results show that shearlets significantly outperform wavelets in inpainting tasks. One of those software packages, www.shearlab.org, even offers the flexibility of usingdifferent parameter for each scale, which is not yet covered by shearlet theory. In this paper, we first introduce universal shearlet systems which are associated with an arbitrary scaling sequence, thereby modeling the previously mentioned flexibility. In addition, this novel construction allows for a smooth transition between wavelets and shearlets and therefore enables us to analyze them in a uniform fashion. For a large class of such scaling sequences, we first prove that the associated universal shearlet systems form band-limited Parseval frames for $L^2(\mathbb{R}^2)$ consisting of Schwartz functions. Secondly, we analyze the performance for inpainting of this class of universal shearlet systems within a distributional model situation using an $\ell^1$-analysis minimization algorithm for reconstruction. Our main result in this part states that, provided the scaling sequence is comparable to the size of the (scale-dependent) gap, nearly-perfect inpainting is achieved at sufficiently fine scales