Related papers: Unitary matrix functions, wavelet algorithms, and …
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
The aim of this paper is to inter-relate several algebraic and analytic objects, such as real-type algebraic curves, quadrature domains, functions on them and rational matrix functions with special properties, and some objects from Operator…
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…
This is the Habilitation Thesis manuscript presented at Besan\c{c}on on January 5, focusing on Matrix Analysis, Matrix Inequalities and Matrix Decompositions. There are also some topics in (Hilbert space) Operator Theory. The text should be…
Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…
Motivated by wavelet analysis, we prove that there is a one-to-one correspondence between the following data: Solutions to $R(h)=h$ where $R$ is a certain non-positive Ruelle transfer operator; Operators that intertwine a certain class of…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
The Delta-variance analysis, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. The implementation presently in use, however, has several shortcomings. We propose and test an…
This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
Recent years have seen a surge in data-driven surrogates for dynamical systems that can be orders of magnitude faster than numerical solvers. However, many machine learning-based models such as neural operators exhibit spectral bias,…
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…
Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical…
Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of webbing and instrumental orchestration are developed. However, the two seemed to be disconnected,…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
We show that translations and dilations of a p-adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p-adic wavelets. In this sense the continuous p-adic wavelet transform…
We give an overview of certain aspects of tractability analysis of multivariate problems. This paper is not intended to give a complete account of the subject, but provides an insight into how the theory works for particular types of…