Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

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Low-light photography produces images with low signal-to-noise ratios due to limited photons. In such conditions, common approximations like the Gaussian noise model fall short, and many denoising techniques fail to remove noise effectively. Although deep- ...

Deep learning has shown remarkable potential for industrial applications, particularly in predictive maintenance and condition monitoring. A key challenge in this domain is prognostics, specifically predicting the Remaining Useful Life (RUL) of assets - a ...

Federated learning (FL) is a machine learning approach where nodes collaboratively train a global model. As more nodes participate in a round of FL, the effectiveness of individual model updates by nodes also diminishes. In this study, we increase the effe ...

We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeability, with an explicit parameter describing the degree of non-exchangeability. Conditional on latent (unobserved) variables, the edges of the n ...

Deriving health indicators of rotating machines is crucial for their maintenance. However, this process is challenging for the prevalent adopted intelligent methods since they may take the whole data distributions, not only introducing noise interference b ...

This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal decomposition have been ...

This thesis focuses on understanding and improving the reasoning capabilities of neural networks. It develops theoretical results and empirical analyses to uncover reasoning potential and limitations, leveraging these insights to guide the design of improv ...

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 ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

Activity-based models offer the potential of a far deeper understanding of daily mobility behaviour than trip-based models. However, activity-based models used both in research and practice have often relied on applying sequential choice models between sub ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are obse ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

In certain cases of astronomical data analysis, the meaningful physical quantity to extract is the ratio R between two data sets. Examples include the lensing ratio, the interloper rate in spectroscopic redshift samples, and the decay rate of gravitational ...

Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models (ECMs) are widely used to characterize the impedance and estimate parameters of electrochemical systems such as batteries. We use a generic ECM with ten parameters grouped to model ...

Water is a crucial resource for all forms of life, yet it is becoming increasingly scarce. A significant portion of water loss in urban and industrial areas is attributed to leaks. Addressing this issue is critical for enhancing efficiency, sustainability, ...

In this article, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained fo ...

Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

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Dark Noise Diffusion: Noise Synthesis for Low-Light Image Denoising

Overcoming Distribution Shifts and Imbalance Challenges in Representation Learning for Deep Regression Models

Harnessing Increased Client Participation with Cohort-Parallel Federated Learning

Tractably modelling dependence in networks beyond exchangeability

Classifier-free diffusion-based weakly-supervised approach for health indicator derivation in rotating machines: Advancing early fault detection and condition monitoring

Deflation-based certified greedy algorithm and adaptivity for bifurcating nonlinear PDEs

Learning to Reason with Neural Networks: Principles and Methods

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

An equilibrated flux a posteriori error estimator for defeaturing problems

OASIS: Optimisation-based Activity Scheduling with Integrated Simultaneous choice dimensions

Spectral Estimators for High-Dimensional Matrix Inference

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

A Shape Derivative Approach to Domain Simplification

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

The elliptical Ornstein-Uhlenbeck process

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

An Unbiased Method of Measuring the Ratio of Two Data Sets

On the use of Cramér-Rao Lower Bound for least-variance circuit parameters identification of Li-ion cells

A two-phase approach for leak detection and localization in water distribution systems using wavelet decomposition and machine learning

Quantization for Decentralized Learning Under Subspace Constraints