Related papers: The Noise Handling Properties of the Talbot Algori…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
Transformers (Vaswani et al., 2017) have brought a remarkable improvement in the performance of neural machine translation (NMT) systems but they could be surprisingly vulnerable to noise. In this work, we try to investigate how noise…
Noise is a part of data whether the data is from measurement, experiment or ... A few techniques are suggested for noise reduction to improve the data quality in recent years some of which are based on wavelet, orthogonalization and neural…
In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy of models with noisy parameters, we consider the problem of…
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…
We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…
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…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…
We have presented a new and alternative algorithm for noise reduction using the methods of discrete wavelet transform and numerical differentiation of the data. In our method the threshold for reducing noise comes out automatically. The…
This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
In this work, we explore a numerical approach for performing the inverse Laplace transformation, with an emphasis on achieving stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
Accurate characterization of quantum systems is essential for the development of quantum technologies, particularly in the noisy intermediate-scale quantum (NISQ) era. While traditional methods for Hamiltonian learning and noise…
Transpilation, particularly noise-aware optimization, is widely regarded as essential for maximizing the performance of quantum circuits on superconducting quantum computers. The common wisdom is that each circuit should be transpiled using…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…