相关论文: Wavelets and Fast Numerical Algorithms

In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…

For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on…

This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…

Leveraging the symmetries inherent to specific data domains for the construction of equivariant neural networks has lead to remarkable improvements in terms of data efficiency and generalization. However, most existing research focuses on…

We present formulas for accurate numerical conversion between functions represented by multiwavelets and their multipole/local expansions with respect to the kernel of the form, $e^{\lambda r}/r$. The conversion is essential for the…

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…

This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…

In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…

Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…

Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…

Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…

The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…

Spatial and spectral approaches are two major approaches for image processing tasks such as image classification and object recognition. Among many such algorithms, convolutional neural networks (CNNs) have recently achieved significant…

The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial…

Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…

Pixel intensity is a widely used feature for clustering and segmentation algorithms, the resulting segmentation using only intensity values might suffer from noises and lack of spatial context information. Wavelet transform is often used…

This is the first paper in a sequence of studies in which we introduce a new type of neural networks (NNs) -- wavelet-based neural networks (WBNNs) -- and study their properties and potential for applications. We begin this study with a…

In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…

An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…

Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…