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Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by solving a sparsity-regularized inverse problem. Traditional CS solvers use iterative optimizers with hand crafted sparsifiers, while early data-driven methods…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Subject-specific cardiovascular models rely on parameter estimation using measurements such as 4D Flow MRI data. However, acquiring high-resolution, high-fidelity functional flow data is costly and taxing for the patient. As a result, there…
A new inversion method for determining near-surface shear currents from a measured wave spectrum is introduced. The method is straightforward to implement and starts from the existing state-of-the-art technique of assigning effective depths…
Traditional supervised bearing fault diagnosis methods rely on massive labelled data, yet annotations may be very time-consuming or infeasible. The fault diagnosis approach that utilizes limited labelled data is becoming increasingly…
In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that,…
By the recent advances in computer technology leading to the invention of more powerful processors, the importance of creating models using data training is even greater than ever. Given the significance of this issue, this work tries to…
Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. On one hand, it can be easily trapped in a local minimum. On the other hand, the inversion results may exhibit strong artifacts and reduced resolution because of…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
The goal of this work is to recover articulatory information from the speech signal by acoustic-to-articulatory inversion. One of the main difficulties with inversion is that the problem is underdetermined and inversion methods generally…
In electrical impedance tomography, we aim to solve the conductivity within a target body through electrical measurements made on the surface of the target. This inverse conductivity problem is severely ill-posed, especially in real…
In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born…
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable…
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…
Full-waveform inversion (FWI) is a method that utilizes seismic data to invert the physical parameters of subsurface media by minimizing the difference between simulated and observed waveforms. Due to its ill-posed nature, FWI is…
In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the…