Jakob Sauer Jørgensen

Pawel Tomasz Pieta, Rasmus Juul Pedersen, Sina Borgi et al.

Gaussian Splatting (GS) has emerged as a dominating technique for image rendering and has quickly been adapted for the X-ray Computed Tomography (CT) reconstruction task. However, despite being on par or better than many of its predecessors, the benefits of GS are typically not substantial enough to motivate a transition from well-established reconstruction algorithms. This paper addresses the most significant remaining limitations of the GS-based approach by introducing FaCT-GS, a framework for fast and flexible CT reconstruction. Enabled by an in-depth optimization of the voxelization and rasterization pipelines, our new method is significantly faster than its predecessors and scales well with projection and output volume size. Furthermore, the improved voxelization enables rapid fitting of Gaussians to pre-existing volumes, which can serve as a prior for warm-starting the reconstruction, or simply as an alternative, compressed representation. FaCT-GS is over 4X faster than the State of the Art GS CT reconstruction on standard 512x512 projections, and over 13X faster on 2k projections. Implementation available at: https://github.com/PaPieta/fact-gs.

Jakob S. Jørgensen, Emil Y. Sidky, Per Christian Hansen et al.

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.

Evangelos Papoutsellis, Casper da Costa-Luis, Daniel Deidda et al.

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.

Chao Zhang, Jasper M. Everink, Jakob Sauer Jørgensen

Gaussian processes (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and can be leveraged to improve model fidelity. Incorporating such constraints into GP models enhances predictive accuracy and reduces uncertainty, but remains a computationally challenging task for high-dimensional problems. In this work, we present a novel virtual point-based framework for building constrained GP models under monotonicity constraints, based on regularized linear randomize-then-optimize (RLRTO), which enables efficient sampling from a constrained posterior distribution by means of solving randomized optimization problems. We also enhance two existing virtual point-based approaches by replacing Gibbs sampling with the No U-Turn Sampler (NUTS) for improved efficiency. A Python implementation of these methods is provided and can be easily applied to a wide range of problems. This implementation is then used to validate the approaches on approximating a range of synthetic functions, demonstrating comparable predictive performance between all considered methods and significant improvements in computational efficiency with the two NUTS methods and especially with the RLRTO method. The framework is further applied to construct surrogate models for systems of differential equations.

Rasmus Dalgas Kongskov, Jakob Sauer Jørgensen, Henning Friis Poulsen et al.

Classical reconstruction methods for phase-contrast tomography consist of two stages: phase retrieval and tomographic reconstruction. A novel algebraic method combining the two was suggested by Kostenko et al. (Opt. Express, 21, 12185, 2013) and preliminary results demonstrating improved reconstruction compared to a two-stage method given. Using simulated free-space propagation experiments with a single sample-detector distance, we thoroughly compare the novel method with the two-stage method to address limitations of the preliminary results. We demonstrate that the novel method is substantially more robust towards noise; our simulations point to a possible reduction in counting times by an order of magnitude.