Generalized L-Spline Wavelet Bases

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The usual explanation of the efficacy of wavelet-based methods hinges on the sparsity of many real-world objects in the wavelet domain. Yet, standard wavelet-shrinkage techniques for sparse reconstruction are not competitive in practice, one reason being t ...

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms and cannot adapt to signals residing on graphs ...

Fault diagnosis plays an essential role in reducing the maintenance costs of rotating machinery manufacturing systems. In many real applications of fault detection and diagnosis, data tend to be imbalanced, meaning that the number of samples for some fault ...

In this paper, the recommended implementation of the post-quantum key exchange SIKE for Cortex-M4 is attacked through power analysis with a single trace by clustering with the k-means algorithm the power samples of all the invocations of the elliptic curve ...

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

A Mach-Zehnder Interferometer (MZI) based optical fibre sensing technique, developed and patented by EPFL, is an efficient and economical way to detect hotspots in High Temperature Superconductor (HTS) applications. Due to the MZI sensitivity being a compo ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

We obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

Capturing high-frequency data concerning the condition of complex systems, e.g. by acoustic monitoring, has become increasingly prevalent. Such high-frequency signals typically contain time dependencies ranging over different time scales and different type ...

Community structure in graph-modeled data appears in a range of disciplines that comprise network science. Its importance relies on the influence it bears on other properties of graphs such as resilience, or prediction of missing connections. Nevertheless, ...

Joint Photographic Experts Group (JPEG) XS is a new International Standard from the JPEG Committee (formally known as ISO/International Electrotechnical Commission (IEC) JTC1/SC29/WG1). It defines an interoperable, visually lossless low-latency lightweight ...

This article summarizes the electromagnetic time-reversal (EMTR) technique for fault location, and further numerically validates its effectiveness when the fault impedance is negligible. In addition, a specific EMTR model considering the fault impedance is ...

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

Nowadays, image and video are the data types that consume most of the resources of modern communication channels, both in fixed and wireless networks. Thus, it is vital to compress visual data as much as possible, while maintaining some target quality leve ...

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...

Generalized L-Spline Wavelet Bases

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The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems

Explicit representations for Banach subspaces of Lizorkin distributions

Stable parameterization of continuous and piecewise-linear functions

Graph Neural Networks With Lifting-Based Adaptive Graph Wavelets

Fault Detection and Diagnosis with Imbalanced and Noisy Data: A Hybrid Framework for Rotating Machinery

Single-Trace Clustering Power Analysis of the Point-Swapping Procedure in the Three Point Ladder of Cortex-M4 SIKE

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Optical fibre based quench detection in HTS applications using machine learning classifiers

A Functional Perspective on Information Measures

Fourier uniqueness and interpolation in Euclidean space

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Collapse-invariant properties of spaces equipped with signals or directions

Learnable Wavelet Packet Transform for Data-Adapted Spectrograms

Graph signal processing tailored for subgraph focus and community structure

JPEG XS-A New Standard for Visually Lossless Low-Latency Lightweight Image Coding

An Effective EMTR-Based High-Impedance Fault Location Method for Transmission Lines

Convex optimization in sums of Banach spaces

Learning-based Image Coding: Early Solutions Reviewing and Subjective Quality Evaluation

Function Integration, Reconstruction And Approximation Using Rank-1 Lattices