Operator Discretization Library (Odl)

Adler, Jonas; Kohr, Holger; Öktem, Ozan

doi:10.5281/zenodo.249479

Cited by 17 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The model parameters in (8) were chosen similar to [19], [8] as γ = 0.9995, ε = 0.01 • max n i=1 ∇v i . The numerical experiments have been carried out in Python using ODL [43]. The line integrals in the PET experiment were computed using the Python module scikit-image [44] and for interpolation we use biquadratic splines from the scipy [40] routine RectBivariateSpline.…”

Section: Numerical Resultsmentioning

confidence: 99%

Robust Image Reconstruction With Misaligned Structural Information

Bungert

Ehrhardt

2020

IEEE Access

View full text Add to dashboard Cite

Multi-modality (or multi-channel) imaging is becoming increasingly important and more widely available, e.g. hyperspectral imaging in remote sensing, spectral CT in material sciences as well as multi-contrast MRI and PET-MR in medicine. Research in the last decades resulted in a plethora of mathematical methods to combine data from several modalities. State-ofthe-art methods, often formulated as variational regularization, have shown to significantly improve image reconstruction both quantitatively and qualitatively. Almost all of these models rely on the assumption that the modalities are perfectly registered, which is not the case in most real world applications. We propose a variational framework which jointly performs reconstruction and registration, thereby overcoming this hurdle. Numerical results show the potential of the proposed strategy for various applications for hyperspectral imaging, PET-MR and multicontrast MRI: typical misalignments between modalities such as rotations, translations, zooms can be effectively corrected during the reconstruction process. Therefore the proposed framework allows the robust exploitation of shared information across multiple modalities under real conditions.Leon Bungert obtained a Master's degree in mathematics at the University of Erlangen, Germany, in 2017. In 2018 he started his PhD at the working group for mathematical imaging and inverse problems at the University of Münster which migrated to the University of Erlangen in October 2018. His research interests include nonlinear eigenvalue problems, partial differential equations, inverse problems, and image reconstruction.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Robust Image Reconstruction With Misaligned Structural Information

Bungert

Ehrhardt

2020

IEEE Access

View full text Add to dashboard Cite

show abstract

“…For AGD we additionally compare with [1]. For PDHG, we modified the implementation in the Python library ODL [25], while we implemented AGD in Julia. All experiments use τ 1 = 1.…”

Section: Numerical Resultsmentioning

confidence: 99%

A generic adaptive restart scheme with applications to saddle point algorithms

Hinder¹,

Lubin²

2020

Preprint

View full text Add to dashboard Cite

We provide a simple and generic adaptive restart scheme for convex optimization that is able to achieve worst-case bounds matching (up to constant multiplicative factors) optimal restart schemes that require knowledge of problem specific constants. The scheme triggers restarts whenever there is sufficient reduction of a distance-based potential function. This potential function is always computable. We apply the scheme to obtain the first adaptive restart algorithm for saddle-point algorithms including primal-dual hybrid gradient (PDHG) and extragradient. The method improves the worst-case bounds of PDHG on bilinear games, and numerical experiments on quadratic assignment problems and matrix games demonstrate dramatic improvements for obtaining high-accuracy solutions. Additionally, for accelerated gradient descent (AGD), this scheme obtains a worst-case bound within 60% of the bound achieved by the (unknown) optimal restart period when high accuracy is desired. In practice, the scheme is competitive with the heuristic of O'Donoghue and Candes [1].Preprint. Under review.

show abstract

“…which can be easily implemented in Operator Discretization Library (ODL). 29 The python code and data can be accessed on https://zenodo.org/badge/ lates tdoi/41751 2547.…”

Section: Algorithmmentioning

confidence: 99%