Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection Methods

Chung, Julianne; Gazzola, Silvia

doi:10.1137/21m1441420

Cited by 5 publications

References 209 publications

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TRIPs-Py: Techniques for regularization of inverse problems in python

Pasha,

Gazzola,

Sanderford

et al. 2024

Numer Algor

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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 introduce test problems arising from a wide range of applications. The solvers available in TRIPs-Py include direct regularization methods (such as truncated singular value decomposition and Tikhonov) and iterative regularization techniques (such as Krylov subspace methods and recent solvers for $$\ell _p$$ ℓ p -$$\ell _q$$ ℓ q formulations, which enforce sparse or edge-preserving solutions and handle different noise types). All our solvers have built-in strategies to define the regularization parameter(s). Some of the test problems in TRIPs-Py arise from simulated image deblurring and computerized tomography, while other test problems model real problems in dynamic computerized tomography. Numerical examples are included to illustrate the usage as well as the performance of the described methods on the provided test problems. To the best of our knowledge, TRIPs-Py is the first Python software package of this kind, which may serve both research and didactical purposes.

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TRIPs-Py: Techniques for regularization of inverse problems in python

Pasha,

Gazzola,

Sanderford

et al. 2024

Numer Algor

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Preliminary validation for an online configuration determination method of a thin film buckling under point contact force

Kim,

2024

Sci Rep

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The authors previously developed an online thin film buckling configuration determination method for a mini basket type mapping catheter prototype, which incorporates eight thin film sensor strips. In the prior study, no external force was applied to the thin film, and only axial displacement was adjusted to induce buckling in the thin film. Extending this prior work, a preliminary methodological validation is conducted for an online configuration determination method of thin film buckling under a point contact force. The overall thin film configuration determination problem is formulated as a constrained optimization problem, involving five variables and five equality constraint functions. Before developing an actual online optimization solver, preliminary numerical calculations, Ansys simulations, and experiments are performed to verify the proposed problem formulation. The comparison between the numerical precalculations, Ansys simulations, and experimental results demonstrated that the proposed problem formulation is consistent with Ansys simulations and experimental outcomes. This indicates that the proposed formulation is capable of calculating accurate solutions using appropriate optimization methodologies.

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Flexible Krylov methods for group sparsity regularization

Chung,

Sabaté Landman

2024

Phys. Scr.

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This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non- overlapping and overlapping groups. Group sparsity regularization refers to a type of structured sparsity regularization, where the goal is to impose additional structure in the regularization process by assigning variables to predefined groups that may represent graph or network structures. Special cases of group sparsity regularization include l1 and isotropic total variation regularization. In this work, we develop hybrid projection methods based on flexible Krylov subspaces, where we first recast the group sparsity regularization term as a sequence of 2-norm penalization terms using adaptive regularization matrices in an iterative reweighted norm fashion. Then, we exploit flexible preconditioning techniques to efficiently incorporate the weight updates. The main advantages of these methods are that they are computationally efficient (leveraging the advantages of flexible methods), they are general (and therefore very easily adaptable to new regularization term choices), and they are able to select the regularization parameters automatically and adaptively (exploiting the advantages of hybrid methods). Extensions to multiple regularization terms and solution decomposition frameworks (e.g., for anomaly detection) are described, and a variety of numerical examples demonstrate both the efficiency and accuracy of the proposed approaches compared to existing solvers.

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Computational Methods for Large-Scale Inverse Problems: A Survey on Hybrid Projection Methods

Cited by 5 publications

References 209 publications

TRIPs-Py: Techniques for regularization of inverse problems in python

TRIPs-Py: Techniques for regularization of inverse problems in python

Preliminary validation for an online configuration determination method of a thin film buckling under point contact force

Flexible Krylov methods for group sparsity regularization

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