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Journal & Preprint Articles

Differentiable Forward and Back-Projector for Rigid Motion Estimation in X-ray Imaging

Published in IEEE Transactions on Biomedical Engineering, 2025

In this work, we propose a framework for differentiable forward and back-projector that enables scalable, accurate, and memory-efficient gradient computation for rigid motion estimation tasks. Unlike existing approaches that rely on auto-differentiation or that are restricted to specific projector types, our method is based on a general analytical gradient formulation for forward/backprojection in the continuous domain. A key insight is that the gradients of both forward and back-projection can be expressed directly in terms of the forward and back-projection operations themselves, providing a unified gradient computation scheme across different projector types. Leveraging this analytical formulation, we develop a discretized implementation with an acceleration strategy that balances computational speed and memory usage. Simulation studies illustrate the numerical accuracy and computational efficiency of the proposed algorithm. Experiments demonstrates the effectiveness of this approach for multiple X-ray imaging tasks we conducted. In 2D/3D registration, the proposed method achieves ∼8× speedup over an existing differentiable forward projector while maintaining comparable accuracy. In motion-compensated analytical reconstruction and cone-beam CT geometry calibration, the proposed method enhances image sharpness and structural fidelity on real phantom data while showing significant efficiency advantages over existing gradient-free and gradient-based solutions. The proposed differentiable projectors enable effective and efficient gradient-based solutions for X-ray imaging tasks requiring rigid motion estimation.

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Joint CT reconstruction of anatomy and implants using a mixed prior model

Published in Journal of Medical Imaging, 2025

Medical implants, often made of dense materials, pose significant challenges to accurate computed tomography (CT) reconstruction, especially near implants due to beam hardening and partial-volume artifacts. Moreover, diagnostics involving implants often require separate visualization for implants and anatomy. In this work, we propose a approach for joint estimation of anatomy and implants as separate volumes using a mixed prior model. We leverage a learning-based prior for anatomy and a sparsity prior for implants to decouple the two volumes. In addition, a hybrid mono-polyenergetic forward model is employed to accommodate the spectral effects of implants, and a multiresolution object model is used to achieve high-resolution implant reconstruction. The reconstruction process alternates between diffusion posterior sampling for anatomy updates and classic optimization for implants and spectral coefficients. Evaluations were performed on emulated cardiac imaging with stent and spine imaging with pedicle screws. The structures of the cardiac stent with 0.25 mm wires were clearly visualized in the implant images, whereas the blooming artifacts around the stent were effectively suppressed in the anatomical reconstruction. For pedicle screws, the proposed algorithm mitigated streaking and beam-hardening artifacts in the anatomy volume, demonstrating significant improvements in SSIM and PSNR compared with frequency-splitting metal artifact reduction and model-based reconstruction on slices containing implants. The proposed mixed prior model coupled with a hybrid spectral and multiresolution model can help to separate spatially and spectrally distinct objects that differ from anatomical features in single-energy CT, improving both image quality and separate visualization of implants and anatomy.

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Joint Temporal and Spectral Processing for Improved Digital Subtraction Angiography Using Photon-Counting Detectors

Published in IEEE Transactions on Biomedical Engineering, 2025

Digital subtraction angiography (DSA) is the gold standard modality for diagnostics and guidance for interventional procedures. Spectral imaging has previously been explored for DSA, but severe noise amplification from material decomposition has impeded clinical adoption. We present a novel joint processing strategy that leverages both temporal and spectral information for material decomposition to address this issue. We develop a model-based material decomposition approach that utilizes the pre- and post-contrast images simultaneously for material estimation. Performance was evaluated on a small-vessel phantom on a test bench with a photon-counting detector. Joint processing was compared with temporal subtraction and previously proposed spectral DSA techniques including hybrid subtraction and conventional three-material decomposition. Additional simulation was performed to investigate performance with perfectly calibrated spectral response and sensitivity to patient motion. The improved conditioning of the proposed method effectively reduces bias and noise in the spectral results and allows three-material decomposition with dual-energy spectral measurements. The method achieved more than an order of magnitude variance reduction compared to previously proposed spectral DSA techniques. Compared to temporal subtraction, a mean variance reduction of 23.9% was achieved in simulation and 10.8% in experimental data. The degree of reduction is object-dependent. Noise reduction achieved in physical experiments is slightly lower than that in simulation, likely due to bias from imperfect spectral calibration. The method is equally sensitive to motion compared to temporal subtraction. The proposed method addresses a major image quality challenge limiting previous approaches and outperforms temporal subtraction. Such improvements facilitate the clinical translation of spectral angiography.

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CTorch: PyTorch-Compatible GPU-Accelerated Auto-Differentiable Projector Toolbox for Computed Tomography

Published in arXiv, 2025

This work introduces CTorch, a PyTorch-compatible, GPU-accelerated, and auto-differentiable projector toolbox designed to handle various CT geometries with configurable projector algorithms. CTorch provides flexible scanner geometry definition, supporting 2D fan-beam, 3D circular cone-beam, and 3D non-circular cone-beam geometries. Each geometry allows view-specific definitions to accommodate variations during scanning. Both flat- and curved-detector models may be specified to accommodate various clinical devices. CTorch implements four projector algorithms: voxel-driven, ray-driven, distance-driven (DD), and separable footprint (SF), allowing users to balance accuracy and computational efficiency based on their needs. All the projectors are primarily built using CUDA C for GPU acceleration, then compiled as Python-callable functions, and wrapped as PyTorch network module. This design allows direct use of PyTorch tensors, enabling seamless integration into PyTorch’s auto-differentiation framework. These features make CTorch an flexible and efficient tool for CT imaging research, with potential applications in accurate CT simulations, efficient iterative reconstruction, and advanced deep-learning-based CT reconstruction.

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Multi-Material Decomposition Using Spectral Diffusion Posterior Sampling

Published in ✨ Featured article @ IEEE Transactions on Biomedical Engineering, 2025

Accurate material decomposition is critical for many spectral CT applications. In this work, we introduce a novel framework—spectral diffusion posterior sampling (Spectral DPS)—designed for one-step reconstruction and multi-material decomposition. Spectral DPS combines sophisticated prior information captured by one-time unconditional network training and an arbitrary analytic physical system model. Built upon the general DPS framework for nonlinear inverse problems, Spectral DPS incorporates several DPS strategies from our previous work, including jumpstart sampling, Jacobian approximation, and multi-step likelihood updates. The effectiveness of Spectral DPS was evaluated on a simulated dual-layer and a kV-switching spectral system as well as on a physical cone-beam CT (CBCT) test bench. In comparison with other diffusion-based algorithms, Spectral DPS showed significant improvements in reducing sampling variability and computational costs over Baseline DPS. Additionally, Spectral DPS outperformed Conditional Denoising Diffusion Probabilistic Model (DDPM), which was trained on specific imaging conditions, in terms of imaging accuracy and robustness across different imaging protocols. In the physical phantom study, Spectral DPS achieved a <1% error in estimating the mean density in a homogeneous region, while effectively avoiding the introduction of false structures seen in Baseline DPS. Both simulation and physical phantom studies demonstrated the superior performance of Spectral DPS on accurate, stable, and fast material decomposition. Significance: Proposed Spectral DPS provided a novel and general material-decomposition framework which can effectively combine learning-based prior and physics-based spectral model. This method can be applied to various spectral CT systems and basis materials.

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CT reconstruction using diffusion posterior sampling conditioned on a nonlinear measurement model

Published in ✨ Cover article @ Journal of Medical Imaging, 2024

Recently, diffusion posterior sampling (DPS), where score-based diffusion priors are combined with likelihood models, has been used to produce high-quality computed tomography (CT) images given low-quality measurements. This technique permits one-time, unsupervised training of a CT prior, which can then be incorporated with an arbitrary data model. However, current methods rely on a linear model of X-ray CT physics to reconstruct. Although it is common to linearize the transmission tomography reconstruction problem, this is an approximation to the true and inherently nonlinear forward model. We propose a DPS method that integrates a general nonlinear measurement model. We implement a traditional unconditional diffusion model by training a prior score function estimator and apply Bayes’ rule to combine this prior with a measurement likelihood score function derived from the nonlinear physical model to arrive at a posterior score function that can be used to sample the reverse-time diffusion process. We develop computational enhancements for the approach and evaluate the reconstruction approach in several simulation studies. The proposed nonlinear DPS provides improved performance over traditional reconstruction methods and DPS with a linear model. Moreover, as compared with a conditionally trained deep learning approach, the nonlinear DPS approach shows a better ability to provide high-quality images for different acquisition protocols. This plug-and-play method allows the incorporation of a diffusion-based prior with a general nonlinear CT measurement model. This permits the application of the approach to different systems, protocols, etc., without the need for any additional training.

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Strategies for CT Reconstruction using Diffusion Posterior Sampling with a Nonlinear Model

Published in arXiv, 2024

Diffusion Posterior Sampling(DPS) methodology is a novel framework that permits nonlinear CT reconstruction by integrating a diffusion prior and an analytic physical system model, allowing for one-time training for different applications. However, baseline DPS can struggle with large variability, hallucinations, and slow reconstruction. This work introduces a number of strategies designed to enhance the stability and efficiency of DPS CT reconstruction. Specifically, jumpstart sampling allows one to skip many reverse time steps, significantly reducing the reconstruction time as well as the sampling variability. Additionally, the likelihood update is modified to simplify the Jacobian computation and improve data consistency more efficiently. Finally, a hyperparameter sweep is conducted to investigate the effects of parameter tuning and to optimize the overall reconstruction performance. Simulation studies demonstrated that the proposed DPS technique achieves up to 46.72% PSNR and 51.50% SSIM enhancement in a low-mAs setting, and an over 31.43% variability reduction in a sparse-view setting. Moreover, reconstruction time is sped up from >23.5 s/slice to <1.5 s/slice. In a physical data study, the proposed DPS exhibits robustness on an anthropomorphic phantom reconstruction which does not strictly follow the prior distribution. Quantitative analysis demonstrates that the proposed DPS can accommodate various dose levels and number of views. With 10% dose, only a 5.60% and 4.84% reduction of PSNR and SSIM was observed for the proposed approach. Both simulation and phantom studies demonstrate that the proposed method can significantly improve reconstruction accuracy and reduce computational costs, greatly enhancing the practicality of DPS CT reconstruction.

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A practical and robust method for beam blocker-based cone beam CT scatter correction

Published in Physics in Medicine & Biology, 2023

In the traditional beam-blocker based cone beam CT (CBCT)scatter correction, the scatter measured in the region shaded by lead strips was multiplied by a correction factor to directly represent the scatter in the unblocked region. The correction factor optimization is a tedious process and lacks an objective stop criterion. To skip the optimization process, an indirect scatter estimation method was developed and validated in phantom imaging. A beam-blocker made of lead strips was mounted between the x-ray source and object for scatter estimation. The primary signal between lead strips in the blocked region was first calculated by subtracting the measured scatter, and then used to calculate the scatter signal in the unblocked region corresponding to the same attenuation path. The calculated scatter signal was smoothed via local filtration and used to correct the measured projection in the unblocked region. Finally, the CBCT was reconstructed via Feldkamp–Davis–Kress algorithm. A Catphan and a head phantom were used to verify the performance of the proposed method in both full- and half-blocker scenarios, and with and without a bow-tie filter. For scans without the bow-tie filter, the CT number error was reduced to 3.97 ± 2.27 and 5.51 ± 3.90 HU in the full- and half-blocker scenarios, respectively, for the Catphan, and to 4.01 ± 2.18 and 7.97 ± 4.05 HU for the head phantom. When the bow-tie filter was applied, the CT number error was reduced to 2.29 ± 1.42 and 6.72 ± 0.77 HU in the full- and half-blocker scenarios, respectively, for the Catphan, and 2.35 ± 1.25 and 4.96 ± 1.89 HU for the head phantom. The proposed method effectively avoids the influence of the inserted beam blocker itself on the scatter intensity estimation, and proves a more practical and robust way for the beam-blocker based scatter correction in CBCT scanning

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Development and validation of a scatter-corrected CBCT image-guided method for cervical cancer brachytherapy

Published in Frontiers in Oncology, 2022

Multiple patient transfers have a nonnegligible impact on the accuracy of dose delivery for cervical cancer brachytherapy. We consider using on-site cone-beam CT (CBCT) to resolve this problem. However, CBCT clinical applications are limited due to inadequate image quality. This paper implements a scatter correction method using planning CT (pCT) prior to obtaining high-quality CBCT images and evaluates the dose calculation accuracy of CBCT-guided brachytherapy for cervical cancer. The CBCT of a self-developed female pelvis phantom and five patients was first corrected using empirical uniform scatter correction in the projection domain and further corrected in the image domain. In both phantom and patient studies, the CBCT image quality before and after scatter correction was evaluated with registered pCT (rCT). Model-based dose calculation was performed using the commercial package Acuros®BV. The dose distributions of rCT-based plans and corrected CBCT-based plans in the phantom and patients were compared using 3D local gamma analysis. A statistical analysis of the differences in dosimetric parameters of five patients was also performed. In both phantom and patient studies, the HU error of selected ROIs was reduced to less than 15 HU. Using the dose distribution of the rCT-based plan as the baseline, the γ pass rate (2%, 2 mm) of the corrected CBCT-based plan in phantom and patients all exceeded 98% and 93%, respectively, with the threshold dose set to 3, 6, 9, and 12 Gy. The average percentage deviation (APD) of D90 of HRCTV and D2cc of OARs was less than 1% between rCT-based and corrected CBCT-based plans. Scatter correction using a pCT prior can effectively improve the CBCT image quality and CBCT-based cervical brachytherapy dose calculation accuracy, indicating promising prospects in both simplified brachytherapy processes and accurate brachytherapy dose delivery.

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Development of an unsupervised cycle contrastive unpaired translation network for MRI-to-CT synthesis

Published in Medical Physics, 2022

The purpose of this work is to develop and evaluate a novel cycle-contrastive unpaired translation network (cycleCUT) for synthetic computed tomography (sCT) generation from T1-weighted magnetic resonance images (MRI). The cycleCUT proposed in this work integrated the contrastive learning module from contrastive unpaired translation network (CUT) into the cycle-consistent generative adversarial network (cycleGAN) framework to effectively achieve unsupervised CT synthesis from MRI. The diagnostic MRI and radiotherapy planning CT images of 24 brain cancer patients were obtained and reshuffled to train the network. For comparison, the traditional cycleGAN and CUT were also implemented. The sCT images were then imported into a treatment planning system to verify their feasibility for radiotherapy planning. The mean absolute error (MAE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM) between the sCT and the corresponding real CT images were calculated. Gamma analysis between sCT- and CT-based dose distributions was also conducted. Quantitative evaluation of an independent test set of six patients showed that the average MAE was 69.62 ± 5.68 Hounsfield Units (HU) for the proposed cycleCUT, significantly (p-value < 0.05) lower than that for cycleGAN (77.02 ± 6.00 HU) and CUT (78.05 ± 8.29). The average PSNR was 28.73 ± 0.46 decibels (dB) for cycleCUT, significantly larger than that for cycleGAN (27.96 ± 0.49 dB) and CUT (27.95 ± 0.69 dB). The average SSIM for cycleCUT (0.918 ± 0.012) was also significantly higher than that for cycleGAN (0.906 ± 0.012) and CUT (0.903 ± 0.015). Regarding gamma analysis, cycleCUT achieved the highest passing rate (97.95 ± 1.24% at the 2%/2 mm criteria and 10% dose threshold) but was not significantly different from the others. The proposed cycleCUT could be effectively trained using unaligned image data, and could generate better sCT images than cycleGAN and CUT in terms of HU number accuracy and fine structural details.

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Planning CT-guided robust and fast cone-beam CT scatter correction using a local filtration technique

Published in Medical Physics, 2021

Cone-beam CT (CBCT) has been widely utilized in image-guided radiotherapy. Planning CT (pCT)-aided CBCT scatter correction could further enhance image quality and extend CBCT application to dose calculation and adaptive planning. Nevertheless, existing pCT-based approaches demand accurate registration between pCT and CBCT, leading to limited imaging performance and increased computational cost when large anatomical discrepancies exist. In this work, we proposed a robust and fast CBCT scatter correction method using local filtration technique and rigid registration between pCT and CBCT (LF-RR). First of all, the pCT was rigidly registered with CBCT, then forward projection was performed on registered pCT to create scatter-free projections. The raw scatter signals were obtained via subtracting the scatter-free projections from the measured CBCT projections. Based on frequency and intensity threshold criteria, reliable scatter signals were selected from the raw scatter signals, and further filtered for global scatter estimation via local filtration technique. Finally, corrected CBCT was reconstructed with the projections generated by subtracting the scatter estimation from the raw CBCT projections using FDK algorithm. The LF-RR method was evaluated via comparison with another pCT-based scatter correction method based on Median and Gaussian filters (MG method).Proposed method was first validated on an anthropomorphic pelvis phantom, and showed satisfied performance on scatter removal even when anatomical mismatches were intentionally created on pCT. The quantitative analysis was further performed on four clinical CBCT images. Compared with the uncorrected CBCT, CBCT corrected by MG with rigid registration (MG-RR), MG with deformable registration (MG-DR), and LF-RR reduced the CT number error from mathematical equation to mathematical equation,mathematical equation and mathematical equation HU for adipose and from mathematical equation to mathematical equation,mathematical equation, mathematical equation3 HU for muscle, respectively. After correction, the spatial non-uniformity (SNU) of CBCT corrected with MG-RR, MG-DR and LF-RR was mathematical equation,mathematical equation, and mathematical equation HU for adipose, and mathematical equation,mathematical equation, and mathematical equation HU for muscle, respectively. Meanwhile, the contrast-to-noise ratio (CNR) between muscle and adipose was increased by a factor of 2.70, 2.89 and 2.56, respectively. Using the LF-RR method, the scatter correction of 656 projections can be finished within 10 s and the corrected volumetric images (200 slices) can be obtained within 2 min. We developed a fast and robust pCT-based CBCT scatter correction method which exploits the local-filtration technique to promote the accuracy of scatter estimation and is resistant to pCT-to-CBCT registration uncertainties. Both phantom and patient studies showed the superiority of the proposed correction in imaging accuracy and computational efficiency, indicating promisingfuture clinical application.

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Fast and effective single-scan dual-energy cone-beam CT reconstruction and decomposition denoising based on dual-energy vectorization

Published in Medical Physics, 2021

Flat-panel detector (FPD) based dual-energy cone-beam computed tomography (DE-CBCT) is a promising imaging technique for dedicated clinical applications. In this paper, we proposed a fully analytical method for fast and effective single-scan DE-CBCT image reconstruction and decomposition. A rotatable Mo filter was inserted between an x-ray source and imaged object to alternately produce low and high-energy x-ray spectra. First, filtered-backprojection (FBP) method was applied on down-sampled projections to reconstruct low and high-energy images. Then, the two images were converted into a vectorized form represented with an amplitude and an argument image. Using amplitude image as a guide, a joint bilateral filter was applied to denoise the argument image. Then, high-quality dual-energy images were recovered from the amplitude image and the denoised argument image. Finally, the recovered dual-energy images were further used for low-noise material decomposition and electron density synthesis. Imaging was conducted on a Catphan®600 phantom and an anthropomorphic head phantom. The proposed method was evaluated via comparison with the traditional two-scan method and a commonly used filtering method (HYPR-LR). On the Catphan®600 phantom, the proposed method successfully reduced streaking artifacts and preserved spatial resolution and noise-power-spectrum (NPS) pattern. In the electron density image, the proposed method increased contrast-to-noise ratio (CNR) by more than 2.5 times and achieved <1.2% error for electron density values. On the anthropomorphic head phantom, the proposed method greatly improved the soft-tissue contrast and the fine detail differentiation ability. In the selected ROIs on different human tissues, the differences between the CT number obtained by the proposed method and that by the two-scan method were less than 4 HU. In the material images, the proposed method suppressed noise by over 75.5% compared with two-scan results, and by over 40.4% compared with HYPR-LR results. Implementation of the whole algorithm took 44.5 s for volumetric imaging, including projection preprocessing, FBP reconstruction, joint bilateral filtering, and material decomposition. Using down-sampled projections in single-scan DE-CBCT, the proposed method could effectively and efficiently produce high-quality DE-CBCT images and low-noise material decomposition images. This method demonstrated superior performance on spatial resolution enhancement, NPS preservation, noise reduction, and electron density accuracy, indicating better prospect in material differentiation and dose calculation.

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Xiao Jiang

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Journal & Preprint Articles