Related papers: On Parseval wavelet frames via Multiresolution Ana…
All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…
Metal-dielectric layered stacks for imaging with sub-wavelength resolution are regarded as linear isoplanatic systems - a concept popular in Fourier Optics and in scalar diffraction theory. In this context, a layered flat lens is a…
Through the use of wavelet based Besov norms, we compute nontrivial multiscale nonlinear features of a given data set so as to enhance the standard Dynamic-Mode Decomposition algorithm. Thus we are able to build sophisticated observables…
We study the universal closest refinement problem on measurable bipartite relations over standard Borel spaces. Given prescribed side measures, the feasible class consists of finite refinement plans concentrated on the relation and carrying…
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
We study refinements between spectral resolutions in an arbitrary II$_1$ factor $\M$ and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
We introduce a new efficient algorithm for Helmholtz problems in perforated domains with the design of the scheme allowing for possibly large wavenumbers. Our method is based upon the Wavelet-based Edge Multiscale Finite Element Method…
We present a novel coarse-to-fine framework that derives a semi-regular multiscale mesh representation of an original input mesh via remeshing. Our approach differs from the conventional mesh wavelet transform strategy in two ways. First,…
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models,…
We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
In this work, wavelet-based filtering operators are constructed by introducing a basic function $D(t_1, t_2, t_3)$ using a general wavelet transform. The cardinal orthogonal scaling functions (COSF) provide an idea to derive the standard…
In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture…
We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while Gabor analysis is associated with unitary irreducible…
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct…
Marchenko focusing functions are in their essence wavefields that satisfy the wave equation subject to a set of boundary, initial, and focusing conditions. Here, we show how Marchenko focusing functions can be modeled by finding the…
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$ setting. This is done in a framework of {\em iterated function system} (IFS) measures;…
The paper deals with the construction of images from visibilities acquired using aperture synthesis instruments: Fourier synthesis, deconvolution, and spectral interpolation/extrapolation. Its intended application is to specific situations…