Related papers: An iterative, dynamically stabilized method of dat…

We describe an iterative unfolding method for experimental data, making use of a regularization function. The use of this function allows one to build an improved normalization procedure for Monte Carlo spectra, unbiased by the presence of…

Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a…

Finite detector resolution and limited acceptance require to apply unfolding methods in high energy physics experiments. Information on the detector resolution is usually given by a set of Monte Carlo events. Based on the experience with a…

Neutrino cross-section measurements are often presented as unfolded binned distributions in "true" variables. The ill-posedness of the unfolding problem can lead to results with strong anti-correlations and fluctuations between bins, which…

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…

Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…

Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…

This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is…

Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior…

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model…

A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of…

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

This paper focuses on signal processing tasks in which the signal is transformed from the signal space to a higher dimensional coefficient space (also called phase space) using a continuous frame, processed in the coefficient space, and…