arXiv subjects

Tristan van Leeuwen

Publications and source records attributed to Tristan van Leeuwen.

At least 19 recordsLinked to original sources

arXiv2026

An invertible generative model for forward and inverse problems

We formulate inverse problems in a Bayesian framework and aim to train an invertible generative model that is capable of simulation (i.e., sampling from the likelihood) and inference (i.e., sampling from the posterior). We call such a generative model a Reversible Simulator. We first construct an explicit instance of a reversible simulator by combining lower and upper triangular normalizing flows associated with conditional sampling into a single invertible map. We then establish basic structural properties of this construction, investigate its non-uniqueness, and derive a variational formulation that enables the generative model to be trained directly from paired samples. Finally, we illustrate the proposed framework on analytically tractable and stylized numerical examples, demonstrating its potential as a unified approach to conditional generative modeling for forward and inverse problems.

stat.ML↗

arXiv2026

Efficient Flow Matching for Sparse-View CT Reconstruction

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.

eess.IV↗

arXiv2026

Equivariance2Inverse: A Practical Self-Supervised CT Reconstruction Method Benchmarked on Real, Limited-Angle, and Blurred Data

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.

eess.IV↗

arXiv2026

Deep Reinforcement Learning for Optimizing Angle Selection and Dose Allocation in CT Reconstruction

Traditional X-ray computed tomography (CT) scanning strategies typically select projection angles uniformly and allocate dose equally. In practice, however, CT scans often need to be fast, radiation-efficient, and adaptive. Sparse-view tomography addresses these requirements by reducing both the number of angles and the total dose budget. Under such constraints, angle selection and dose allocation should be information-driven, with more dose assigned to informative directions. To this end, we propose a dose-aware acquisition and reconstruction framework that combines a PWLS-PnP reconstruction backbone with an RL-based strategy for adaptive angle selection, explicitly accounting for angle-dependent photon statistics. Numerical experiments show that the proposed approach improves overall reconstruction quality and enhances defect detectability compared with conventional strategies, particularly when only a small number of projections or a constrained dose budget is available.

physics.med-ph↗

arXiv2026

Data-Driven Filter Design for Flexible and Noise-Robust Tomographic Imaging

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 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.

math.NA↗

arXiv2025

Quasi-static in vivo elastography from internal displacement information only

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.

physics.med-ph↗

arXiv2025

Inverse scattering for Schrödinger equation in the frequency domain via data-driven reduced order modeling

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 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 non-linear 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.

math.NA↗

arXiv2025

Exploring Out-of-distribution Detection for Sparse-view Computed Tomography with Diffusion Models

Recent works demonstrate the effectiveness of diffusion models as unsupervised solvers for inverse imaging problems. Sparse-view computed tomography (CT) has greatly benefited from these advancements, achieving improved generalization without reliance on measurement parameters. However, this comes at the cost of potential hallucinations, especially when handling out-of-distribution (OOD) data. To ensure reliability, it is essential to study OOD detection for CT reconstruction across both clinical and industrial applications. This need further extends to enabling the OOD detector to function effectively as an anomaly inspection tool. In this paper, we explore the use of a diffusion model, trained to capture the target distribution for CT reconstruction, as an in-distribution prior. Building on recent research, we employ the model to reconstruct partially diffused input images and assess OOD-ness through multiple reconstruction errors. Adapting this approach for sparse-view CT requires redefining the notions of ``input'' and ``reconstruction error''. Here, we use filtered backprojection (FBP) reconstructions as input and investigate various definitions of reconstruction error. Our proof-of-concept experiments on the MNIST dataset highlight both successes and failures, demonstrating the potential and limitations of integrating such an OOD detector into a CT reconstruction system. Our findings suggest that effective OOD detection can be achieved by comparing measurements with forward-projected reconstructions, provided that reconstructions from noisy FBP inputs are conditioned on the measurements. However, conditioning can sometimes lead the OOD detector to inadvertently reconstruct OOD images well. To counter this, we introduce a weighting approach that improves robustness against highly informative OOD measurements, albeit with a trade-off in performance in certain cases.

eess.IV↗

arXiv2025

Sequential Experimental Design for X-Ray CT Using Deep Reinforcement Learning

In X-ray Computed Tomography (CT), projections from many angles are acquired and used for 3D reconstruction. To make CT suitable for in-line quality control, reducing the number of angles while maintaining reconstruction quality is necessary. Sparse-angle tomography is a popular approach for obtaining 3D reconstructions from limited data. To optimize its performance, one can adapt scan angles sequentially to select the most informative angles for each scanned object. Mathematically, this corresponds to solving an optimal experimental design (OED) problem. OED problems are high-dimensional, non-convex, bi-level optimization problems that cannot be solved online, i.e., during the scan. To address these challenges, we pose the OED problem as a partially observable Markov decision process in a Bayesian framework, and solve it through deep reinforcement learning. The approach learns efficient non-greedy policies to solve a given class of OED problems through extensive offline training rather than solving a given OED problem directly via numerical optimization. As such, the trained policy can successfully find the most informative scan angles online. We use a policy training method based on the Actor-Critic approach and evaluate its performance on 2D tomography with synthetic data.

eess.IV↗

arXiv2025

Dynamic Angle Selection in X-Ray CT: A Reinforcement Learning Approach to Optimal Stopping

In industrial X-ray Computed Tomography (CT), the need for rapid in-line inspection is critical. Sparse-angle tomography plays a significant role in this by reducing the required number of projections, thereby accelerating processing and conserving resources. Most existing methods aim to balance reconstruction quality and scanning time, typically relying on fixed scan durations. Adaptive adjustment of the number of angles is essential; for instance, more angles may be required for objects with complex geometries or noisier projections. The concept of optimal stopping, which dynamically adjusts this balance according to varying industrial needs, remains overlooked. Building on our previous work, we integrate optimal stopping into sequential Optimal Experimental Design (sOED) and Reinforcement Learning (RL). We propose a novel method for computing the policy gradient within the Actor-Critic framework, enabling the development of adaptive policies for informative angle selection and scan termination. Additionally, we investigate the gap between simulation and real-world applications in the context of the developed learning-based method. Our trained model, developed using synthetic data, demonstrates reliable performance when applied to experimental X-ray CT data. This approach enhances the flexibility of CT operations and expands the applicability of sparse-angle tomography in industrial settings.

cs.CV↗

arXiv2025

Phasebook: A Survey of Selected Open Problems in Phase Retrieval

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.

cs.IT↗

arXiv2025

PtyGenography: using generative models for regularization of the phase retrieval problem

In phase retrieval and similar inverse problems, the stability of solutions across different noise levels is crucial for applications. One approach to promote it is using signal priors in a form of a generative model as a regularization, at the expense of introducing a bias in the reconstruction. In this paper, we explore and compare the reconstruction properties of classical and generative inverse problem formulations. We propose a new unified reconstruction approach that mitigates overfitting to the generative model for varying noise levels.

stat.ML↗

arXiv2024

An Analysis of Constraint-Relaxation in PDE-Based Inverse Problems

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which the inherent non-linearity of the problem is an important one. In this paper, we focus on a relaxed formulation of the PDE-constrained optimization problem and provide an in-depth analysis of it. Starting from an infinite-dimensional formulation of the inverse problem with discrete data, we propose a general framework for the analysis and discretisation of such problems. The relaxed formulation of the PDE-constrained optimization problem is shown to reduce to a weighted non-linear least-squares problem. The weight matrix turns out to be the Gram matrix of solutions of the PDE and, in some cases, can be estimated directly from the measurements. The latter observation points to a potential way to unify recently proposed data-driven reduced-order models for inverse problems with PDE-constrained optimization. We provide a number of representative case studies and numerical examples to illustrate our findings.

math.OC↗

arXiv2024

Derivative-free stochastic bilevel optimization for inverse problems

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.

math.OC↗

arXiv2024

AC-IND: Sparse CT reconstruction based on attenuation coefficient estimation and implicit neural distribution

Computed tomography (CT) reconstruction plays a crucial role in industrial nondestructive testing and medical diagnosis. Sparse view CT reconstruction aims to reconstruct high-quality CT images while only using a small number of projections, which helps to improve the detection speed of industrial assembly lines and is also meaningful for reducing radiation in medical scenarios. Sparse CT reconstruction methods based on implicit neural representations (INRs) have recently shown promising performance, but still produce artifacts because of the difficulty of obtaining useful prior information. In this work, we incorporate a powerful prior: the total number of material categories of objects. To utilize the prior, we design AC-IND, a self-supervised method based on Attenuation Coefficient Estimation and Implicit Neural Distribution. Specifically, our method first transforms the traditional INR from scalar mapping to probability distribution mapping. Then we design a compact attenuation coefficient estimator initialized with values from a rough reconstruction and fast segmentation. Finally, our algorithm finishes the CT reconstruction by jointly optimizing the estimator and the generated distribution. Through experiments, we find that our method not only outperforms the comparative methods in sparse CT reconstruction but also can automatically generate semantic segmentation maps.

eess.IV↗

arXiv2024

Quantifying the effect of X-ray scattering for data generation in real-time defect detection

Background: X-ray imaging is widely used for the non-destructive detection of defects in industrial products on a conveyor belt. In-line detection requires highly accurate, robust, and fast algorithms. Deep Convolutional Neural Networks (DCNNs) satisfy these requirements when a large amount of labeled data is available. To overcome the challenge of collecting these data, different methods of X-ray image generation are considered. Objective: Depending on the desired degree of similarity to real data, different physical effects should either be simulated or can be ignored. X-ray scattering is known to be computationally expensive to simulate, and this effect can greatly affect the accuracy of a generated X-ray image. We aim to quantitatively evaluate the effect of scattering on defect detection. Methods: Monte-Carlo simulation is used to generate X-ray scattering distribution. DCNNs are trained on the data with and without scattering and applied to the same test datasets. Probability of Detection (POD) curves are computed to compare their performance, characterized by the size of the smallest detectable defect. Results: We apply the methodology to a model problem of defect detection in cylinders. When trained on data without scattering, DCNNs reliably detect defects larger than 1.3 mm, and using data with scattering improves performance by less than 5%. If the analysis is performed on the cases with large scattering-to-primary ratio ($1 < SPR < 5$), the difference in performance could reach 15% (approx. 0.4 mm). Conclusion: Excluding the scattering signal from the training data has the largest effect on the smallest detectable defects, and the difference decreases for larger defects. The scattering-to-primary ratio has a significant effect on detection performance and the required accuracy of data generation.

eess.IV↗

arXiv2024

Quantitative phase imaging via a multimode fiber

Label-free quantitative phase imaging is a vital tool for optical microscopy and metrology applications. A hair-thin multimode fiber stands out as a very attractive platform for minimally invasive imaging. Here we propose and experimentally demonstrate a non-interferometric non-iterative approach for high-speed high-resolution label-free quantitative phase imaging via a multimode fiber, unlocking multiple applications in life science and bioimaging.

physics.optics↗

arXiv2024

Experimental Validation of Ultrasound Beamforming with End-to-End Deep Learning for Single Plane Wave Imaging

Ultrafast ultrasound imaging insonifies a medium with one or a combination of a few plane waves at different beam-steered angles instead of many focused waves. It can achieve much higher frame rates, but often at the cost of reduced image quality. Deep learning approaches have been proposed to mitigate this disadvantage, in particular for single plane wave imaging. Predominantly, image-to-image post-processing networks or fully learned data-to-image neural networks are used. Both construct their mapping purely data-driven and require expressive networks and large amounts of training data to perform well. In contrast, we consider data-to-image networks which incorporate a conventional image formation techniques as differentiable layers in the network architecture. This allows for end-to-end training with small amounts of training data. In this work, using f-k migration as an image formation layer is evaluated in-depth with experimental data. We acquired a data collection designed for benchmarking data-driven plane wave imaging approaches using a realistic breast mimicking phantom and an ultrasound calibration phantom. The evaluation considers global and local image similarity measures and contrast, resolution and lesion detectability analysis. The results show that the proposed network architecture is capable of improving the image quality of single plane wave images on all evaluation metrics. Furthermore, these image quality improvements can be achieved with surprisingly little amounts of training data.

eess.IV↗