Related papers: Continuous Shearlet Tight Frames
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth…
Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and image reconstruction. In this work, we consider the representation of spatio-temporal data such as temporal…
Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models…
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…
Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as…
Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse…
Let $H$ be an infinite-dimensional separable Hilbert space and let $(X,d,\mu)$ be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small scale. We prove that every bounded continuous tight frame…
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…
We make precise some results on the cloaking of displacement fields in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosserat and Willis frameworks are shown to be equivalent to…
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
We investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general anisotropic $N$-function, which is not necessarily of power type and need not satisfy the $\Delta_2$ nor the $\nabla _2$-condition. Fully anisotropic,…
We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
For every set $S$ of finite measure in $\mathbb{R}$ we construct a discrete set of real frequencies $\Lambda$ such that the exponential system $\{\exp(i\lambda t),\lambda\in\Lambda\}$ is a frame in $L^2(S)$
We consider the 2d and 3d many body Schr\"odinger equations in the presence of anisotropic switchable quadratic traps. We extend and improve the collapsing estimates in Klainerman-Machedon [24] and Kirkpatrick-Schlein-Staffilani [23].…
Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of…
The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis.…
Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series…
To effectively capture singularities in high-dimensional data and functions, multivariate compactly supported tight framelets, having directionality and derived from refinable box splines, are of particular interest in both theory and…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…