Related papers: Samplets: Wavelet concepts for scattered data

The central idea of compressed sensing is to exploit the fact that most signals of interest are sparse in some domain and use this to reduce the number of measurements to encode. However, if the sparsity of the input signal is not precisely…

Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…

This paper introduces a Deep Scattering network that utilizes Dual-Tree complex wavelets to extract translation invariant representations from an input signal. The computationally efficient Dual-Tree wavelets decompose the input signal into…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

Exascale computing promises quantities of data too large to efficiently store and transfer across networks in order to be able to analyze and visualize the results. We investigate Compressive Sensing (CS) as a way to reduce the size of the…

Dataset condensation aims to condense a large dataset with a lot of training samples into a small set. Previous methods usually condense the dataset into the pixels format. However, it suffers from slow optimization speed and large number…

Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…

We propose a data reduction technique for scattered data based on statistical sampling. Our void-and-cluster sampling technique finds a representative subset that is optimally distributed in the spatial domain with respect to the blue noise…

Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…

Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral…

This letter proposes a novel distributed compressed estimation scheme for sparse signals and systems based on compressive sensing techniques. The proposed scheme consists of compression and decompression modules inspired by compressive…

Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard…

Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace…

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These…

In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…