Shearlet systems have so far been only considered as a means to analyze L2-functions defined on R2, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial differential equations the function to be analyzed or efficiently encoded is typically defined on a non-rectangular shaped bounded domain. Motivated by these applications, in...

In this paper we provide a construction of multiscale systems on a bounded domain Ω ⊂ R coined boundary shearlet systems, which satisfy several properties advantageous for applications to imaging science and numerical analysis of partial differential equations. More precisely, we construct a boundary shearlet system that forms a frame for L(Ω) with controllable frame bounds and admits optimally...

Under the linear approximation model for error diffusion halftoning, a shearlet-based inverse halftoning (SIH) algorithm is proposed. The SIH algorithm performs inverse halftoning by first inverting the modelspecified convolution operator and then reducing the residual color noise using scalar shearlet-domain thresholding. The optimal thresholds are derived by using the maximum a posteriori rul...

Convolutional Neural Networks (CNNs) are a type of deep neural network which have performed well at image and audio classification. One approach to understanding the success of CNNs is Mallat’s scattering transform, which formalizes the observation that the filters learned by a CNN have wavelet-like structure. The resulting transform generates a representation that is approximately translation ...

Several empirical results appeared in the literature during the last decade have shown that it is often possible to separate images and other multidimensional data into geometrically distinct constituents. A rigorous mathematical analysis of the geometric separation problem in the two-dimensional setting was recently introduced by Donoho and Kutyniok [6], who proposed a mathematical framework t...

We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields infinite coupling, partition function can be written as full contraction of tensor network consisting coupled local numeric and Grassmann tensors. To evaluate to compute observables, we develop higher-order renormalization group...