Tristan van Leeuwen

Purpose: To develop and validate a method for time‐resolved 3D imaging and strain analysis that enables quantification of dynamic in vivo muscle deformations from aperiodic continuous motion. Theory and Methods: Controlled deformations were induced in the thigh muscles of eight healthy volunteers using a pneumatic pressure cuff, both under passive conditions and during isometric muscle contractions. An iterative reconstruction approach based on the Spectro‐Dynamic MRI framework was formulated for joint reconstruction of time‐resolved 3D images and velocity fields from highly undersampled k‐space data at 1.4 Hz. The accuracy of the results was evaluated against fully sampled images, acquired under static conditions with similar deformations. Octahedral shear strain (OSS) values were computed from the estimated motion fields. Mean OSS values were calculated for all thigh muscles, and differences in the mean OSS values between passive and isometric contraction conditions were assessed. Results: The reconstructed time‐resolved images closely matched the fully sampled validation images and the estimated motion fields accurately captured the deformations. Isometric muscle contraction resulted in reduced displacements and lower mean OSS values compared with the passive condition. The largest reduction in mean OSS value was consistently observed in the hamstring muscles, which become stiffer during isometric knee flexion. Conclusion: Our proposed reconstruction approach enables robust time‐resolved 3D strain estimates in muscles using data from a single motion repetition. This method provides new opportunities for investigating the temporal evolution of in vivo displacements and strains in a dynamic setting.

This study presents two workflows for leveraging longitudinal computed tomography (CT) datasets when developing deep learning-based detection systems for gradually developing postharvest disorders. Workflow 1 (Longitudinal Benchmarking) benchmarks neural networks by training and testing them on images from different stages of disorder progression. It examines the trade-off between detecting a disorder early or accurately and evaluates whether neural networks can generalize across time points. Workflow 2 (Longitudinal eXplainable Artificial Intelligence (XAI) Heatmaps) provides heatmaps that indicate how changes over time affect the outcomes of neural networks. It uses image registration to align an earlier-acquired image and then uses it as a baseline when calculating the heatmap. The workflows are demonstrated on a dataset of ‘Braeburn’ apples that were CT-scanned multiple times while developing internal browning during controlled-atmosphere (CA) storage and shelf life. The Longitudinal Benchmarking workflow was used to investigate whether images acquired immediately after CA storage can be used to predict the eventual browning after a shelf-life period, which is highly relevant in industrial practice. Moreover, the longitudinal XAI heatmaps avoided artifacts caused by out-of-distribution baselines or identical baseline regions, which occurred with conventional black or zero baselines.

Deep learning has shown impressive results in reducing noise and artifacts in X-ray computed tomography (CT) reconstruction. Self-supervised CT reconstruction methods are especially appealing for real-world applications because they require no ground truth training examples. However, these methods involve a simplified X-ray physics model during training, which may make inaccurate assumptions, for example, about scintillator blurring, the scanning geometry, or the distribution of the noise. As a result, they can be less robust to real-world imaging circumstances. In this paper, we review the model assumptions of six recent self-supervised CT reconstruction methods. Based on this, we combined concepts of the Robust Equivariant Imaging and Sparse2Inverse methods in a new self-supervised CT reconstruction method called Equivariance2Inverse that is robust to scintillator blurring and limited-angle data. We benchmarked Equivariance2Inverse and the existing methods on the real-world 2DeteCT dataset and on synthetic data with and without scintillator blurring and a limited-angle scanning geometry. The results of our benchmark show that methods that assume that the noise is pixel-wise independent do not perform well on data with scintillator blurring. Moreover, they show that when the distribution of objects is rotationally invariant, this invariance can be used to reduce artifacts in limited-angle reconstructions.

While filtered back-projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a data-driven approach for learning FBP filters and projection weights directly from training data, with the goal of improving robustness without sacrificing computational efficiency. The resulting reconstructions adapt naturally to the noise level and acquisition geometry, while retaining the speed and simplicity of classical back-projection. The proposed method can be formulated as a regularized optimization problem for a linear inverse operator, which allows us to establish existence, uniqueness, and stability of the learned solution. From a spectral viewpoint, the learned filters act as data-adaptive gain functions that explicitly balance noise amplification and bias, in close analogy to a regularized pseudo-inverse. Experiments in both 2D and 3D show consistent improvements over conventional FBP and Feldkamp–Davis–Kress (FDK) in different case studies. Finally, we show that filters trained on synthetic laminography data generalize well to real-world measurements, delivering image quality comparable to advanced iterative methods without the high computational cost.

In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schrödinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a projection of the Schrödinger operator onto a subspace spanned by its solution snapshots at certain wavenumbers. Provided the measurements are performed at these wavenumbers, the ROM can be constructed in a data-driven manner from the measurements on a surface surrounding the scatterers. Once the ROM is computed, the scattering potential can be estimated using nonlinear optimization that minimizes the ROM misfit. Such an approach typically outperforms the conventional methods based on data misfit minimization. We develop two variants of ROM-based algorithms for inverse scattering and test them on a synthetic example in two spatial dimensions.

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and investigate their generalization properties when confronted with unseen data. This approach dictates a statistical approach to inverse problems, calling for stochastic optimization methods. In order to learn model and regularisation parameters simultaneously, we develop in this paper a stochastic bilevel optimization approach in which the lower level problem represents a variational reconstruction method formulated as a convex non-smooth optimization problem, depending on the observed sample. The upper level problem represents the learning task of the regularisation parameters. Combining the lower level and the upper level problem leads to a stochastic non-smooth and non-convex optimization problem, for which standard gradient-based methods are not straightforward to implement. Instead, we develop a unified and flexible methodology, building on a derivative-free approach, which allows us to solve the bilevel optimization problem only with samples of the objective function values. We perform a complete complexity analysis of this scheme. Numerical results on signal denoising and experimental design demonstrate the computational efficiency and the generalization properties of our method.

Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in theoretical signal processing and applied harmonic analysis. This survey paper is an outcome of the recent workshop Phase Retrieval in Mathematics and Applications (PRiMA) (held on August 5–9 2024 at the Lorentz Center in Leiden, The Netherlands) that brought together experts working on theoretical and practical aspects of the phase retrieval problem with the purpose to formulate and explore essential open problems in the field.

As disease often alters the structural properties of soft tissue, noninvasive elastography techniques have emerged to quantitatively assess in vivo mechanical properties. Magnetic Resonance Elastography (MRE) based on dynamic deformations is the standard technique for imaging mechanical properties, but the viscoelastic nature of soft tissue makes the results dependent on the actuation frequency, which can be limiting. In this proof-of-principle study we propose a noise robust framework for reconstructing relative stiffness properties from quasi-static in vivo displacement fields captured on a physiological time scale. The acquisition is performed using a pneumatic pressure cuff to induce tissue deformation in a controlled manner. The reconstruction does not require boundary information which is generally hard to access in vivo nor spatial derivatives of displacement fields that are known to amplify noise. The validity of our framework is corroborated with in silico experiments on a numerical phantom. In vivo experiments on the thigh of a volunteer demonstrate the repeatability of the method. As an application, the quantitative change in muscle stiffness during isometric knee flexion is investigated which yielded physiologically meaningful results.