arXiv subjects

Georg Schramm

Publications and source records attributed to Georg Schramm.

16 recordsLinked to original sources

arXiv2025

Object independent scatter sensitivities for PET, applied to scatter estimation through fast Monte Carlo simulation

Scattered coincidences introduce quantitative bias in positron emission tomography (PET) and must be compensated during reconstruction. Conventional scatter estimates typically rely on simplified cylindrical scanner models that omit detector physics. Incorporating detector sensitivities for scatter is challenging because scattered events exhibit less constrained properties, such as incidence angles, compared to true coincidences. We integrated a 5D single-photon detection probability lookup table (LUT) accounting for photon energy, incidence angle, and detector location into the simulator logic. The resulting scatter sinogram is scaled by a precomputed, LUT-specific scatter sensitivity sinogram. Scatter was simulated using MCGPU-PET, a fast Monte Carlo (MC) simulator with a simplified scanner model, and applied to phantom data from a simulated GE Signa PET/MR in GATE. We evaluated three scenarios: (1) high-count MC simulations from a known activity distribution; (2) limited-count simulations; and (3) joint estimation of activity and scatter under low-count conditions. The method was also tested on two real Signa PET/MR acquisitions. In scenario 1, scatter-compensated reconstructions achieved <1% global bias in all active regions. In scenario 2, noisy scatter estimates caused positive bias, but Gaussian smoothing restored accuracy to scenario 1 levels. In scenario 3, joint estimation maintained <1% bias in nearly all regions. For real scans, the MC-based scatter estimate closely matched the vendor-provided scatter estimate. This proof-of-concept demonstrates that scatter sensitivity modeling can enhance simulators by incorporating detector physics. It supports the feasibility of using fast MC simulations for real scans, offering improved accuracy and robustness to acquisition noise in clinical PET reconstruction.

physics.med-ph↗

arXiv2025

Fast PET Reconstruction with Variance Reduction and Prior-Aware Preconditioning

We investigate subset-based optimization methods for positron emission tomography (PET) image reconstruction incorporating a regularizing prior. PET reconstruction methods that use a prior, such as the relative difference prior (RDP), are of particular relevance, as they are widely used in clinical practice and have been shown to outperform conventional early-stopped and post-smoothed ordered subsets expectation maximization (OSEM). Our study evaluates these methods on both simulated data and real brain PET scans from the 2024 PET Rapid Image Reconstruction Challenge (PETRIC), where the main objective was to achieve RDP-regularized reconstructions as fast as possible, making it an ideal benchmark. Our key finding is that incorporating the effect of the prior into the preconditioner is crucial for ensuring fast and stable convergence. In extensive simulation experiments, we compare several stochastic algorithms -- including Stochastic Gradient Descent (SGD), Stochastic Averaged Gradient Amelior\'e (SAGA), and Stochastic Variance Reduced Gradient (SVRG) -- under various algorithmic design choices and evaluate their performance for varying count levels and regularization strengths. The results show that SVRG and SAGA outperformed SGD, with SVRG demonstrating a slight overall advantage. The insights gained from these simulations directly contributed to the design of our submitted algorithms, which formed the basis of the winning contribution to the PETRIC 2024 challenge.

physics.med-ph↗

arXiv2025

DeepInverse: A Python package for solving imaging inverse problems with deep learning

DeepInverse is an open-source PyTorch-based library for solving imaging inverse problems. The library covers all crucial steps in image reconstruction from the efficient implementation of forward operators (e.g., optics, MRI, tomography), to the definition and resolution of variational problems and the design and training of advanced neural network architectures. In this paper, we describe the main functionality of the library and discuss the main design choices.

eess.IV↗

arXiv2025

Improved energy-based scatter estimation by incorporating local energy spectra and accelerating the parametric fitting

PET requires accurate, precise, and efficient scatter correction techniques. Conventional scatter estimation typically relies on tail-fitted single-scatter simulation (SSS) strategy. However, the accuracy of tail-fitted SSS is limited, for example, by mismatches between the attenuation image and the PET emission data or by the presence of activity outside the FOV. These shortcomings can be addressed using energy-based scatter estimation (EBSE), as recently proposed by Efthimiou et al. and Hamill et al. The aim of this work is to 1. improve the accuracy of EBSE by accounting for the LOR dependence of the energy spectrum of unscattered photons, 2. improve the computational speed of EBSE through better initialization and a more efficient optimization algorithm. The proposed improved EBSE method models the energy probability density function (PDF) of both single and multiple scattered photons, and incorporates a position-dependent energy PDF for unscattered photons. These energy PDFs form the basis of two forward models used for scatter estimation based on 2D energy histograms. The performance of these models were evaluated using GATE Monte Carlo simulations and a NEMA phantom acquisition on a GE SIGNA PET/MR scanner. Furthermore, we assessed the stability of EBSE across the forward models by varying the number of counts in the 2D energy histograms via data mashing. EBSE outperformed tail-fitted SSS, particularly in regions near out-of-FOV activity. Our GATE simulations showed that incorporating a local energy for unscattered photons improves off-center regional quantification by approximately 2% points. Additionally, improved initialization combined with the NEGML optimizer enabling execution on a mashed TOF sinogram in 12 minutes on six-core CPU. The proposed method enhances both the accuracy and computational efficiency of EBSE, making it well-suited for clinical applications.

physics.med-ph↗

arXiv2025

Exact Parameter Identification in PET Pharmacokinetic Modeling: Extension to the Reversible Two Tissue Compartment Model

This paper addresses the problem of recovering tracer kinetic parameters from multi-region measurement data in quantitative PET imaging using the reversible two tissue compartment model. Its main result is an extension of our previous work on the irreversible two tissue compartment model. In analogy to our previous work, we show that also in the (practically highly relevant) reversible case, most tracer kinetic parameters can be uniquely identified from standard PET measurements (without additional full blood sample analysis that is usually performed in practice) and under reasonable assumptions. In addition, unique identifiability of all parameters is shown provided that additional measurements from the (uncorrected) total arterial blood tracer concentration (which can be obtained from standard PET measurements or from a simple blood sample analysis) are available.

math.OC↗

arXiv2024

Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET

Whole-body PET imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated TOF PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as 3 clinical FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but static attenuation correction, and with our proposed methods. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with static attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware.

physics.med-ph↗

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↗

arXiv2023

PARALLELPROJ -- An open-source framework for fast calculation of projections in tomography

In this article, we introduce, a novel open-source framework designed for efficient parallel computation of projections in tomography leveraging either multiple CPU cores or GPUs. This framework efficiently implements forward and back projection functions for both sinogram and listmode data, utilizing Joseph's method, which is further extended to encompass time-of-flight (TOF) PET projections. Our evaluation involves a series of tests focusing on PET image reconstruction using data sourced from a state-of-the-art clinical PET/CT system. We thoroughly benchmark the performance of the projectors in non-TOF and TOF, sinogram, and listmode employing multi CPU-cores, hybrid CPU/GPU, and exclusive GPU mode. Moreover, we also investigate the timing of non-TOF sinogram projections calculated in STIR (Software for Tomographic Image Reconstruction) which recently integrated parallelproj as one of its projection backends. Our results indicate that the exclusive GPU mode provides acceleration factors between 25 and 68 relative to the multi-CPU-core mode. Furthermore, we demonstrate that OSEM listmode reconstruction of state-of-the-art real-world PET data sets is achievable within a few seconds using a single consumer GPU.

physics.med-ph↗

arXiv2023

Resolution enhancement, noise suppression, and joint T2* decay estimation in dual-echo sodium-23 MR imaging using anatomically-guided reconstruction

Purpose: Sodium MRI is challenging because of the low tissue concentration of the 23 Na nucleus and its extremely fast biexponential transverse relaxation rate. In this article, we present an iterative reconstruction framework using dual-echo 23Na data and exploiting anatomical prior information (AGR) from high-resolution, low-noise, 1 H MR images. This framework enables the estimation and modeling of the spatially-varying signal decay due to transverse relaxation during readout (AGRdm), which leads to images of better resolution and reduced noise resulting in improved quantification of the reconstructed 23Na images. Methods: The proposed framework was evaluated using reconstructions of 30 noise realizations of realistic simulations of dual echo twisted projection imaging (TPI) 23 Na data. Moreover, three dual echo 23 Na TPI brain data sets of healthy controls acquired on a 3T Siemens Prisma system were reconstructed using conventional reconstruction, AGR and AGRdm. Results: Our simulations show that compared to conventional reconstructions, AGR and AGRdm show improved bias-noise characteristics in several regions of the brain. Moreover, AGR and AGRdm images show more anatomical detail and less noise in the reconstructions of the experimental data sets. Compared to AGR and the conventional reconstruction, AGRdm shows higher contrast in the sodium concentration ratio between gray and white matter and between gray matter and the brain stem. Conclusion: AGR and AGRdm generate 23 Na images with high resolution, high levels of anatomical detail, and low levels of noise, potentially enabling high-quality 23 Na MR imaging at 3T.

physics.med-ph↗

arXiv2023

Exact Parameter Identification in PET Pharmacokinetic Modeling Using the Irreversible Two Tissue Compartment Model

This work is concerned with the identifiability of metabolic parameters from multi-region measurement data in quantitative PET imaging. It shows that, for the frequently used two-tissue compartment model and under reasonable assumptions, it is possible to uniquely identify metabolic tissue parameters from standard PET measurements, without the need of additional concentration measurements from blood samples. This result, which holds in the idealized, noiseless scenario, indicates that costly concentration measurements from blood samples in quantitative PET imaging can be avoided in principle. The connection to noisy measurement data is made via a consistency result, showing that exact reconstruction is maintained in the vanishing noise limit. Numerical experiments with a regularization approach are further carried out to support these analytic results in an application example.

math.OC↗

arXiv2022

Fast and memory-efficient reconstruction of sparse Poisson data in listmode with non-smooth priors with application to time-of-flight PET

Complete time of flight (TOF) sinograms of state-of-the-art TOF PET scanners have a large memory footprint. Currently, they contain ~4e9 data bins which amount to ~17GB in 32bit floating point precision. Using iterative algorithms to reconstruct such enormous TOF sinograms becomes increasingly challenging due to the memory requirements and the computation time needed to evaluate the forward model for every data bin. This is especially true for more advanced optimization algorithms such as the SPDHG algorithm which allows for the use of non-smooth priors using subsets with guaranteed convergence. SPDHG requires the storage of additional sinograms in memory, which severely limits its application to data sets from state-of-the-art TOF PET systems. Motivated by the generally sparse nature of the TOF sinograms, we propose and analyze a new listmode (LM) extension of the SPDHG algorithm for reconstruction of sparse data following a Poisson distribution. The new algorithm is evaluated based on 2D and 3D simulations, and a real dataset acquired on a recent TOF PET/CT system. The performance of the newly proposed LM SPDHG algorithm is compared against the conventional sinogram SPDHG and the listmode EM-TV algorithm. We show that the speed of convergence of LM-SPDHG is equivalent the original SPDHG using binned data. However, we find that for a TOF PET system with 400ps TOF resolution, LM-SPDHG reduces the required memory from ~56GB to 0.7GB for a short dynamic frame with 1e7 counts and to 12.4GB for a long static acquisition with 5e8 counts. In contrast to SPDHG, the reduced memory requirements of LM-SPDHG enable a pure GPU implementation on state-of-the-art GPUs which will substantially accelerate reconstruction times. This in turn will allow the application of LM-SPDHG in routine clinical practice where short reconstruction times are crucial.

physics.med-ph↗

arXiv2021

One-step inversion algorithms for spectral CT, with application to dynamic Cone Beam CT

Dual Energy Cone Beam Computed Tomography (DE-CBCT) is a promising technique for several medical applications, including dynamic angiography. Recently, a dynamical two-step method has been proposed : first, the water and iodine projections are computed from the multi-energy sinograms, then, a dynamic image of the iodine contrast is reconstructed using 4D Total-Variation (TV) constrained reconstruction from the iodine projections. In contrast to the 2-step methods, one-step methods use a model relating directly the multi-material images to the multi-energy sinograms. This kind of methods are well-known to reduce the noise correlation between the material images by avoiding the intermediate decomposition step, but request to solve an non-convex large scale optimization problem which can be challenging. In this work we use the Non-Linear Primal-Dual Hybrid Gradient Method (NL-PDHGM) optimization framework to propose two versions of a one-step method which is based on an empirical model : the first one is a version which considers the multi-material images as static object whereas the second version is developped for a specific application with a static water image and a dynamic iodine image consisting of a series of 3D iodine images associated to different time points. This last version is developped to obtain the evolution of the iodine concentration in the blood vessels during a single CBCT scan. To evaluate the proposed one-step methods we used simulations which consider a CBCT system with dual layer spectral detector and a brain phantom with a static and a dynamic vascular tree. The proposed one-step methods are compared with 2-step methods.

physics.med-ph↗

arXiv2021

Proceedings of the 16th Virtual International Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine

These proceedings contain the presented papers at the 16th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine 2021, which was to be held in Leuven, Belgium, but had to be transformed in a virtual meeting because of the covid-19 pandemic. Fully3D is one of the major forums for presentation of new results in the field of 3D image reconstruction, primarily with applications in x-ray computer tomography, PET and SPECT. Over the life-time of the meeting the focus has shifted to reflect recent developments in the field. Many of the major developments in fully 3D PET and SPECT imaging were first presented at Fully3D, as were the key results for analytic reconstruction methods in cone beam x-ray CT. Similarly, in the 2021 meeting a broad range of topics has been presented. As expected, deep learning methods are being used increasingly: they are used as post-processing tools or incorporated in the reconstruction, often aiming at improved noise and/or artifact suppression.

physics.med-ph↗

arXiv2018

Regional accuracy of ZTE-based attenuation correction in static and dynamic brain PET/MR

Accurate MR-based attenuation correction (MRAC) is essential for quantitative PET/MR imaging of the brain. In this study, we analyze the regional bias caused by MRAC based on Zero-Echo-Time MR images (ZTEAC) compared to CT-based AC (CTAC) in static and dynamic PET imaging. In addition the results are compared to the performance of the current default Atlas-based AC (AtlasAC) implemented in the GE SIGNA PET/MR. Methods: Thirty static [18F]FDG and 11 dynamic [18}F]PE2I acquisitions from a GE SIGNA PET/MR were reconstructed using ZTEAC (using a research tool, GE Healthcare), single-subject AtlasAC (the current default AC in GE's SIGNA PET/MR) and CTAC (from a PET/CT acquisition of the same day). In the 30 static [18F]FDG reconstructions, the bias caused by ZTEAC and AtlasAC in the mean uptake of 85 anatomical volumes of interest (VOIs) of the Hammers' atlas was analyzed in PMOD. For the 11 dynamic [18}F]PE2I reconstructions, the bias caused by ZTEAC and AtlasAC in the non displaceable binding potential BPnd in the striatum was calculated with cerebellum as the reference region and a simplified reference tissue model. Results: The regional bias caused by ZTEAC in the static [18F]FDG reconstructions ranged from -8.0% to +7.7% (mean 0.1%, SD 2.0%). For AtlasAC this bias ranged from -31.6% to +16.6% (mean -0.4%, SD 4.3%). The bias caused by AtlasAC showed a clear gradient in the cranio-caudal direction (-4.2% in the cerebellum, +6.6% in the left superior frontal gyrus). The bias in the striatal BPnd for the [18F]PE2I reconstructions ranged from -0.8% to +4.8% (mean 1.5%, SD 1.4%) using ZTEAC and from -0.6% to +9.4% using AtlasAC (mean 4.2%, SD 2.6%). Conclusion: ZTEAC provides excellent quantitative accuracy for static and dynamic brain PET/MR, comparable to CTAC, and is clearly superior to the default AtlasAC currently implemented in the GE SIGNA PET/MR.

physics.med-ph↗

arXiv2013

Neutron total cross section measurements of gold and tantalum at the nELBE photoneutron source

Neutron total cross sections of $^{197}$Au and $^\text{nat}$Ta have been measured at the nELBE photoneutron source in the energy range from 0.1 - 10 MeV with a statistical uncertainty of up to 2 % and a total systematic uncertainty of 1 %. This facility is optimized for the fast neutron energy range and combines an excellent time structure of the neutron pulses (electron bunch width 5 ps) with a short flight path of 7 m. Because of the low instantaneous neutron flux transmission measurements of neutron total cross sections are possible, that exhibit very different beam and background conditions than found at other neutron sources.

nucl-ex↗

arXiv2011

Description of dipole strength in heavy nuclei in conformity with their quadrupole degrees of freedom

In conformity to new findings about the widespread occurrence of triaxiality arguments are given in favor of a description of the giant dipole resonance in heavy nuclei by the sum of three Lorentzians. This TLO parameterization allows a strict use of resonance widths Γ in accordance to the theoretically founded power law relation to the resonance energy. No additional variation of Γ with the photon energy and no violation of the sum rule are necessary to obtain a good agreement to nuclear photo-effect, photon scattering and radiative capture data. Photon strength other than E1 has a small effect, but the influence of the level density on photon emission probabilities needs further investigation.

nucl-ex↗