Mirjeta Pasha
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View article: Projected iterated Tikhonov in general form with adaptive choice of the regularization parameter
Projected iterated Tikhonov in general form with adaptive choice of the regularization parameter Open
Tikhonov regularization is commonly used in the solution of linear discrete ill-posed problems. It is known that iterated Tikhonov regularization often produces approximate solutions of higher quality than (standard) Tikhonov regularizatio…
View article: Priorconditioned Sparsity-Promoting Projection Methods for Deterministic and Bayesian Linear Inverse Problems
Priorconditioned Sparsity-Promoting Projection Methods for Deterministic and Bayesian Linear Inverse Problems Open
High-quality reconstructions of signals and images with sharp edges are needed in a wide range of applications. To overcome the large dimensionality of the parameter space and the complexity of the regularization functional, {sparisty-prom…
View article: Efficient Dynamic Image Reconstruction with motion estimation
Efficient Dynamic Image Reconstruction with motion estimation Open
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous comput…
View article: Krylov Subspace Based FISTA‐Type Methods for Linear Discrete Ill‐Posed Problems
Krylov Subspace Based FISTA‐Type Methods for Linear Discrete Ill‐Posed Problems Open
Several iterative soft‐thresholding algorithms, such as FISTA, have been proposed in the literature for solving regularized linear discrete inverse problems that arise in various applications in science and engineering. These algorithms ar…
View article: TRIPs-Py: Techniques for regularization of inverse problems in python
TRIPs-Py: Techniques for regularization of inverse problems in python Open
In this paper we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to …
View article: TRIPs-Py: Techniques for Regularization of Inverse Problems in Python
TRIPs-Py: Techniques for Regularization of Inverse Problems in Python Open
In this paper, we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to…
View article: TRIPs-Py: Techniques for Regularization of Inverse Problems in Python
TRIPs-Py: Techniques for Regularization of Inverse Problems in Python Open
In this paper, we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to…
View article: Tensor Completion with BMD Factor Nuclear Norm Minimization
Tensor Completion with BMD Factor Nuclear Norm Minimization Open
This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficiently compress third-order spatiotemporal data. Using the BM…
View article: Recycling MMGKS for large-scale dynamic and streaming data
Recycling MMGKS for large-scale dynamic and streaming data Open
Reconstructing high-quality images with sharp edges requires the use of edge-preserving constraints in the regularized form of the inverse problem. The use of the $\ell_q$-norm on the gradient of the image is a common such constraint. For …
View article: Spatiotemporal Besov Priors for Bayesian Inverse Problems
Spatiotemporal Besov Priors for Bayesian Inverse Problems Open
Fast development in science and technology has driven the need for proper statistical tools to capture special data features such as abrupt changes or sharp contrast. Many inverse problems in data science require spatiotemporal solutions d…
View article: Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization
Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization Open
The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro method for solving separable nonlinear least squares problems with general-form…
View article: Sparse representation learning derives biological features with explicit gene weights from the Allen Mouse Brain Atlas
Sparse representation learning derives biological features with explicit gene weights from the Allen Mouse Brain Atlas Open
Unsupervised learning methods are commonly used to detect features within transcriptomic data and ultimately derive meaningful representations of biology. Contributions of individual genes to any feature however becomes convolved with each…
View article: Randomized Algorithms for Rounding in the Tensor-Train Format
Randomized Algorithms for Rounding in the Tensor-Train Format Open
The tensor-train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equati…
View article: A computational framework for edge-preserving regularization in dynamic inverse problems
A computational framework for edge-preserving regularization in dynamic inverse problems Open
We devise efficient methods for dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change in time. Our goal is to solve for all the quantities of interest simultaneously. We c…
View article: Preface
Preface Open
Computed Tomography (CT) brought about a revolutionary advancement in imaging technology that has transformed the landscape of industry and diagnostic medicine.This non-invasive imaging technique provides cross-sectional views of objects f…
View article: Efficient learning methods for large-scale optimal inversion design
Efficient learning methods for large-scale optimal inversion design Open
In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can b…
View article: Bayesian Spatiotemporal Modeling for Inverse Problems
Bayesian Spatiotemporal Modeling for Inverse Problems Open
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or bi…
View article: The Image Deblurring Problem: Matrices, Wavelets, and Multilevel Methods
The Image Deblurring Problem: Matrices, Wavelets, and Multilevel Methods Open
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for sol…
View article: Sparse Representation Learning Derives Biological Features with Explicit Gene Weights from the Allen Mouse Brain Atlas
Sparse Representation Learning Derives Biological Features with Explicit Gene Weights from the Allen Mouse Brain Atlas Open
Unsupervised learning methods are commonly used to detect features within transcriptomic data and ultimately derive meaningful representations of biology. Contributions of individual genes to any feature however becomes convolved with each…
View article: Randomized algorithms for rounding in the Tensor-Train format
Randomized algorithms for rounding in the Tensor-Train format Open
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential equati…
View article: Efficient learning methods for large-scale optimal inversion design
Efficient learning methods for large-scale optimal inversion design Open
In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can b…
View article: A Krylov subspace type method for Electrical Impedance Tomography
A Krylov subspace type method for Electrical Impedance Tomography Open
Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many application…
View article: Efficient edge-preserving methods for dynamic inverse problems
Efficient edge-preserving methods for dynamic inverse problems Open
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
View article: An $\ell_p$ Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems
An $\ell_p$ Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems Open
The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro for large-scale separable nonlinear inverse problems that promotes edge-preserv…
View article: An 𝓁 p Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems.
An 𝓁 p Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems. Open
The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro for large-scale separable nonlinear inverse problems that promotes edge-preserv…
View article: Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures
Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures Open
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to…
View article: Optimal Transport for Parameter Identification of Steady-State Chaotic Dynamics
Optimal Transport for Parameter Identification of Steady-State Chaotic Dynamics Open
Parameter identification determines the essential system parameters required to build real-world dynamical systems by fusing crucial physical relationships and experimental data. However, the data-driven approach faces main difficulties, s…