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An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
Within the area of applied harmonic analysis, various multiscale systems such as wavelets, ridgelets, curvelets, and shearlets have been introduced and successfully applied. The key property of each of those systems are their (optimal)…
The paper shows that under some mild conditions $n$-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on $n$-dimensional spheres…
Coded aperture imaging systems have recently shown great success in recovering scene depth and extending the depth-of-field. The ideal pattern, however, would have to serve two conflicting purposes: 1) be broadband to ensure robust…
A family of Parseval periodic wavelet frames is constructed. The family has optimal time-frequency localization (in the sense of the Breitenberger uncertainty constant) with respect to a family parameter and it has the best currently known…
We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
Convolutional neural networks (CNN) have had unprecedented success in medical imaging and, in particular, in medical image segmentation. However, despite the fact that segmentation results are closer than ever to the inter-expert…
This article studies sufficient conditions on families of approximating kernels which provide $N$--term approximation errors from an associated nonlinear approximation space which match the best known orders of $N$--term wavelet expansion.…
In this paper, we propose a general framework for constructing tight framelet systems on graphs with localized supports based on partition trees. Our construction of framelets provides a simple and efficient way to obtain the orthogonality…
Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…
To construct models of large, multivariate complex systems, such as those in biology, one needs to constrain which variables are allowed to interact. This can be viewed as detecting "local" structures among the variables. In the context of…
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and erasures, and as such, have great potential…
Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
As an alternative to conventional multi-pixel cameras, single-pixel cameras enable images to be recorded using a single detector that measures the correlations between the scene and a set of patterns. However, to fully sample a scene in…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…