Related papers: Measurable multiresolution systems, endomorphisms,…
In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The…
The increasing use of multiple sensors, which produce a large amount of multi-dimensional data, requires efficient representation and classification methods. In this paper, we present a new method for multi-dimensional data classification…
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by solving a sparsity-regularized inverse problem. Traditional CS solvers use iterative optimizers with hand crafted sparsifiers, while early data-driven methods…
Machine learning (ML) can represent processes unresolved in coarse-resolution Earth system models (ESMs) by learning from high-resolution climate data. Such ML parameterization approaches have been primarily tested in idealized setups where…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
A new method for directly sampling the neutron resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches,…
The ideal imaging system would efficiently capture information about all fundamental properties light: intensity, direction, wavelength, and polarization. Most common imaging systems only map the spatial degrees of freedom of light onto a…
Hyperspectral (HS) images provide fine spectral resolution but have limited spatial resolution, whereas multispectral (MS) images capture finer spatial details but have fewer bands. HS-MS fusion aims to integrate HS and MS images to…
A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace…
Wavelet functions allow the sparse and efficient representation of a signal at different scales. Recently the application of wavelets to the denoising of maps of cosmic microwave background (CMB) fluctuations has been proposed. The…
The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important…
Future wireless services, such as the metaverse require high information rate, reliability, and low latency. Multi-user wireless systems can meet such requirements by utilizing the abundant terahertz bandwidth with a massive number of…
The generalization ability of Convolutional neural networks (CNNs) for biometrics drops greatly due to the adverse effects of various occlusions. To this end, we propose a novel unified framework integrated the merits of both CNNs and…
Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on…
We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
Multitask learning (MTL) aims to learn multiple tasks simultaneously through the interdependence between different tasks. The way to measure the relatedness between tasks is always a popular issue. There are mainly two ways to measure…
Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse-graining extremely difficult. We here address this problem by…
As a newly emerging advance in deep generative models, diffusion models have achieved state-of-the-art results in many fields, including computer vision, natural language processing, and molecule design. The remote sensing (RS) community…