arXiv subjects

Jakob S. Jørgensen

Publications and source records attributed to Jakob S. Jørgensen.

15 recordsLinked to original sources

arXiv2026

A Modular Approach to Stochastic Optimisation for Inverse Problems Using the Core Imaging Library

The Core Imaging Library (CIL) is an open-source versatile Python framework for solving inverse problems with special emphasis on imaging applications such as computed tomography (CT), using a plug-in architecture for data and operators, interfacing to toolboxes such as ASTRA, TIGRE and SIRF. A key component of CIL is its optimisation module enabling users to flexibly combine mathematical operators and functionals to form smooth and non-smooth optimisation problems and solve these with a range of first-order algorithms. The present work introduces an expansion of CIL with a new modular framework for stochastic optimisation, allowing researchers to easily use a variety of existing stochastic optimisation algorithms as well form new ones by combining modular building blocks. Users can flexibly configure algorithmic components, adapt to diverse problem structures, and experiment with various sampling and step size strategies. Rather than individual black-box implementations of each fixed algorithm with significant redundancies, our design is modular providing building blocks that can be flexibly combined to realise a wealth of algorithm instances. The framework is particularly well-suited for large-scale applications, where stochastic methods offer notable computational advantages over deterministic approaches. To demonstrate its versatility and practical utility, we present experiments on real-world datasets from imaging inverse problems, such as X-Ray CT and Positron Emission Tomography (PET) reconstruction. In summary, the presented software expansion aims to support the research community with a robust, extensible optimisation suite for developing, testing, and benchmarking stochastic methods for inverse problems.

math.OC↗

arXiv2025

A Computational Framework and Implementation of Implicit Priors in Bayesian Inverse Problems

Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are commonly used, but they require prior and likelihood densities to be explicitly provided. In cases where expressing the prior explicitly is challenging, implicit priors offer an alternative, encoding prior information indirectly. These priors have gained increased interest in recent years, with methods like Plug-and-Play (PnP) priors and Regularized Linear Randomize-then-Optimize (RLRTO) providing computationally efficient alternatives to standard MCMC algorithms. However, the abstract concept of implicit priors for Bayesian inverse problems is yet to be systematically explored and little effort has been made to unify different kinds of implicit priors. This paper presents a computational framework for implicit priors and their distinction from explicit priors. We also introduce an implementation of various implicit priors within the CUQIpy Python package for Computational Uncertainty Quantification in Inverse Problems. Using this implementation, we showcase several implicit prior techniques by applying them to a variety of different inverse problems from image processing to parameter estimation in partial differential equations.

cs.MS↗

arXiv2024

Democratizing Uncertainty Quantification

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.

cs.MS↗

arXiv2024

Stochastic Optimisation Framework using the Core Imaging Library and Synergistic Image Reconstruction Framework for PET Reconstruction

We introduce a stochastic framework into the open--source Core Imaging Library (CIL) which enables easy development of stochastic algorithms. Five such algorithms from the literature are developed, Stochastic Gradient Descent, Stochastic Average Gradient (-Amélioré), (Loopless) Stochastic Variance Reduced Gradient. We showcase the functionality of the framework with a comparative study against a deterministic algorithm on a simulated 2D PET dataset, with the use of the open-source Synergistic Image Reconstruction Framework. We observe that stochastic optimisation methods can converge in fewer passes of the data than a standard deterministic algorithm.

math.NA↗

arXiv2022

Structural Gaussian Priors for Bayesian CT reconstruction of Subsea Pipes

A non-destructive testing (NDT) application of X-ray computed tomography (CT) is inspection of subsea pipes in operation via 2D cross-sectional scans. Data acquisition is time-consuming and costly due to the challenging subsea environment. Reducing the number of projections in a scan can yield time and cost savings, but compromises the reconstruction quality, if conventional reconstruction methods are used. In this work we take a Bayesian approach to CT reconstruction and focus on designing an effective prior to make use of available structural information about the pipe geometry. We propose a new class of structural Gaussian priors to enforce expected material properties in different regions of the reconstructed image based on independent Gaussian priors in combination with global regularity through a Gaussian Markov Random Field (GMRF) prior. Numerical experiments with synthetic and real data show that the proposed structural Gaussian prior can reduce artifacts and enhance contrast in the reconstruction compared to using only a global GMRF prior or no prior at all. We show how the resulting posterior distribution can be efficiently sampled even for large-scale images, which is essential for practical NDT applications.

math.NA↗

arXiv2022

Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm

The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application to CT when using unmatched back-projector/projector pairs and when applying preconditioning. The GMRES algorithm is demonstrated on a 3D CT image reconstruction problem where it is seen that use of unmatched projection matrices does not prevent convergence, while using an unmatched pair in the related conjugate gradients for least-squares (CGLS) algorithm leads to divergent iteration. Implementation of preconditioning using GMRES is also demonstrated.

physics.med-ph↗

arXiv2022

A Bayesian Approach to CT Reconstruction with Uncertain Geometry

Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that may not be valid in practice. One such assumption is that the exact projection geometry is known. The projection geometry describes the relative location of the radiation source, object, and detector for each projection. However, in practice, the geometric parameters used to describe the position and orientation of the radiation source, object, and detector are estimated quantities with uncertainty. A failure to accurately estimate the geometry may lead to reconstructions with severe misalignment artifacts that significantly decrease their scientific or diagnostic value. We propose a novel reconstruction method that jointly estimates the reconstruction and the projection geometry. The reconstruction method is based on a Bayesian approach that yields a point estimate for the reconstruction and geometric parameters and, in addition, provides valuable information regarding their uncertainty. This is achieved by approximately sampling from the joint posterior distribution of the reconstruction and projection geometry using a hierarchical Gibbs sampler. Using real tomographic data, we demonstrate that the proposed reconstruction method significantly reduces misalignment artifacts. Compared with two commonly used alignment methods, our proposed method achieves comparable or better results under challenging conditions.

math.NA↗

arXiv2021

Core Imaging Library -- Part II: Multichannel reconstruction for dynamic and spectral tomography

The newly developed Core Imaging Library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularised reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g., dynamic and spectral. We formalise different optimisation problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL's capabilities for designing state of the art reconstruction methods through case studies and code snapshots.

physics.med-ph↗

arXiv2021

Core Imaging Library -- Part I: a versatile Python framework for tomographic imaging

We present the Core Imaging Library (CIL), an open-source Python framework for tomographic imaging with particular emphasis on reconstruction of challenging datasets. Conventional filtered back-projection reconstruction tends to be insufficient for highly noisy, incomplete, non-standard or multi-channel data arising for example in dynamic, spectral and in situ tomography. CIL provides an extensive modular optimisation framework for prototyping reconstruction methods including sparsity and total variation regularisation, as well as tools for loading, preprocessing and visualising tomographic data. The capabilities of CIL are demonstrated on a synchrotron example dataset and three challenging cases spanning golden-ratio neutron tomography, cone-beam X-ray laminography and positron emission tomography.

math.OC↗

arXiv2021

Enhanced hyperspectral tomography for bioimaging by spatiospectral reconstruction

Here we apply hyperspectral bright field imaging to collect computed tomographic images with excellent energy resolution (800 eV), applying it for the first time to map the distribution of stain in a fixed biological sample through its characteristic K-edge. Conventionally, because the photons detected at each pixel are distributed across as many as 200 energy channels, energy-selective images are characterised by low count-rates and poor signal-to-noise ratio. This means high X-ray exposures, long scan times and high doses are required to image unique spectral markers. Here, we achieve high quality energy-dispersive tomograms from low dose, noisy datasets using a dedicated iterative reconstruction algorithm. This exploits the spatial smoothness and inter-channel structural correlation in the spectral domain using two carefully chosen regularisation terms. For a multi-phase phantom, a reduction in scan time of 36 times is demonstrated. Spectral analysis methods including K-edge subtraction and absorption step-size fitting are evaluated for an ex vivo, single (iodine)-stained biological sample, where low chemical concentration and inhomogeneous distribution can affect soft tissue segmentation and visualisation. The reconstruction algorithms are available through the open-source Core Imaging Library. Taken together, these tools offer new capabilities for visualisation and elemental mapping, with promising applications for multiply-stained biological specimens.

physics.med-ph↗

arXiv2021

Crystalline phase discriminating neutron tomography using advanced reconstruction methods

Time-of-flight neutron imaging offers complementary attenuation contrast to X-ray computed tomography (CT), coupled with the ability to extract additional information from the variation in attenuation as a function of neutron energy (time of flight) at every point (voxel) in the image. In particular Bragg edge positions provide crystallographic information and therefore enable the identification of crystalline phases directly. Here we demonstrate Bragg edge tomography with high spatial and spectral resolution. We propose a new iterative tomographic reconstruction method with a tailored regularisation term to achieve high quality reconstruction from low-count data, where conventional filtered back-projection (FBP) fails. The regularisation acts in a separated mode for spatial and spectral dimensions and favours characteristic piece-wise constant and piece-wise smooth behaviour in the respective dimensions. The proposed method is compared against FBP and a state-of-the-art regulariser for multi-channel tomography on a multi-material phantom. The proposed new regulariser which accommodates specific image properties outperforms both conventional and state-of-the-art methods and therefore facilitates Bragg edge fitting at the voxel level. The proposed method requires significantly shorter exposure to retrieve features of interest. This in turn facilitates more efficient usage of expensive neutron beamline time and enables the full utilisation of state-of-the-art high resolution detectors.

physics.med-ph↗

arXiv2014

How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray CT

We introduce phase-diagram analysis, a standard tool in compressed sensing, to the X-ray CT community as a systematic method for determining how few projections suffice for accurate sparsity-regularized reconstruction. In compressed sensing a phase diagram is a convenient way to study and express certain theoretical relations between sparsity and sufficient sampling. We adapt phase-diagram analysis for empirical use in X-ray CT for which the same theoretical results do not hold. We demonstrate in three case studies the potential of phase-diagram analysis for providing quantitative answers to questions of undersampling: First we demonstrate that there are cases where X-ray CT empirically performs comparable with an optimal compressed sensing strategy, namely taking measurements with Gaussian sensing matrices. Second, we show that, in contrast to what might have been anticipated, taking randomized CT measurements does not lead to improved performance compared to standard structured sampling patterns. Finally, we show preliminary results of how well phase-diagram analysis can predict the sufficient number of projections for accurately reconstructing a large-scale image of a given sparsity by means of total-variation regularization.

math.OC↗

arXiv2014

Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized x-ray CT

We study recoverability in fan-beam computed tomography (CT) with sparsity and total variation priors: how many underdetermined linear measurements suffice for recovering images of given sparsity? Results from compressed sensing (CS) establish such conditions for, e.g., random measurements, but not for CT. Recoverability is typically tested by checking whether a computed solution recovers the original. This approach cannot guarantee solution uniqueness and the recoverability decision therefore depends on the optimization algorithm. We propose new computational methods to test recoverability by verifying solution uniqueness conditions. Using both reconstruction and uniqueness testing we empirically study the number of CT measurements sufficient for recovery on new classes of sparse test images. We demonstrate an average-case relation between sparsity and sufficient sampling and observe a sharp phase transition as known from CS, but never established for CT. In addition to assessing recoverability more reliably, we show that uniqueness tests are often the faster option.

math.OC↗

arXiv2014

Empirical average-case relation between undersampling and sparsity in x-ray CT

In x-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is motivated by recent progress in compressed sensing (CS). However, the CS framework provides neither guarantees of accurate CT reconstruction, nor any relation between sparsity and a sufficient number of measurements for recovery, i.e., perfect reconstruction from noise-free data. We consider reconstruction through 1-norm minimization, as proposed in CS, from data obtained using a standard CT fan-beam sampling pattern. In empirical simulation studies we establish quantitatively a relation between the image sparsity and the sufficient number of measurements for recovery within image classes motivated by tomographic applications. We show empirically that the specific relation depends on the image class and in many cases exhibits a sharp phase transition as seen in CS, i.e. same-sparsity image require the same number of projections for recovery. Finally we demonstrate that the relation holds independently of image size and is robust to small amounts of additive Gaussian noise.

math.NA↗

arXiv2013

First-order convex feasibility algorithms for iterative image reconstruction in X-ray CT

Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this article, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for efficient algorithms for their solution -- thereby facilitating the IIR algorithm design process. An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization.

physics.med-ph↗