Related papers: Hybrid Projection Methods with Recycling for Inver…
This paper delves into an in-depth exploration of the Variable Projection (VP) algorithm, a powerful tool for solving separable nonlinear optimization problems across multiple domains, including system identification, image processing, and…
We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…
We present a method for projecting an input image into the space of a class-conditional generative neural network. We propose a method that optimizes for transformation to counteract the model biases in generative neural networks.…
This paper documents a computational implementation of a {\em projection and rescaling algorithm} for finding most interior solutions to the pair of feasibility problems \[ \text{find} \; x\in L\cap\mathbb{R}^n_{+} \;\;\;\; \text{ and } \;…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Constrained convex optimization problems arise naturally in many real-world applications. One strategy to solve them in an approximate way is to translate them into a sequence of convex feasibility problems via the recently developed level…
In large-scale X-ray computed tomography (CT), matrix-free iterative methods are essential due to the prohibitive cost of explicitly forming the system matrix. In practice, forward projectors and backprojectors are often implemented with…
Augmented Krylov subspace methods aid in accelerating the convergence of a standard Krylov subspace method by including additional vectors in the search space. A residual projection framework based on residual (Petrov-) Galerkin constraints…
Focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid is discussed. For the uniform grid the model sensitivity matrices exhibit block Toeplitz Toeplitz…
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,…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…
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 be…
Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational…
Hybrid X-ray and magnetic resonance (MR) imaging promises large potential in interventional medical imaging applications due to the broad variety of contrast of MRI combined with fast imaging of X-ray-based modalities. To fully utilize the…
LSQR and LSMR are iterative methods, based on the Golub-Kahan bidiagonalization algorithm, widely used for large-scale linear least squares problems. FLSQR and FLSMR are flexible variants of LSQR and LSMR, respectively, based on a flexible…
Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…