DRACO: Differentiable Reconstruction for Arbitrary CBCT Orbits

This paper introduces a novel method for reconstructing cone beam computed tomography (CBCT) images for arbitrary orbits using a differentiable shift-variant filtered backprojection (FBP) neural network. Traditional CBCT reconstruction methods for arbitrary orbits, like iterative reconstruction algorithms, are computationally expensive and memory-intensive. The proposed method addresses these challenges by employing a shift-variant FBP algorithm optimized for arbitrary trajectories through a deep learning approach that adapts to a specific orbit geometry. This approach overcomes the limitations of existing techniques by integrating known operators into the learning model, minimizing the number of parameters, and improving the interpretability of the model. The proposed method is a significant advancement in interventional medical imaging, particularly for robotic C-arm CT systems, enabling faster and more accurate CBCT reconstructions with customized orbits. Especially this method can also be used for the analytical reconstruction of non-continuous orbits like circular plus arc. The experimental results demonstrate that the proposed method significantly accelerates the reconstruction process compared to conventional iterative algorithms. It achieves comparable or superior image quality, as evidenced by metrics such as the mean squared error (MSE), the peak signal-to-noise ratio (PSNR), and the structural similarity index measure (SSIM). The validation experiments show that the method can handle data from different trajectories, demonstrating its flexibility and robustness across different scan geometries. Our method demonstrates a significant improvement, particularly for the sinusoidal trajectory, achieving a 38.6% reduction in MSE, a 7.7% increase in PSNR, and a 5.0% improvement in SSIM. Furthermore, the computation time for reconstruction was reduced by more than 97%.

Data-driven Modeling in Metrology -- A Short Introduction, Current Developments and Future Perspectives

Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These models generally represent the correlation between the quantity being measured and all other pertinent quantities. Such relationships are used to construct measurement systems that can interpret measurement data to generate conclusions and predictions about the measurement system itself. Classic models are typically analytical, built on fundamental physical principles. However, the rise of digital technology, expansive sensor networks, and high-performance computing hardware have led to a growing shift towards data-driven methodologies. This trend is especially prominent when dealing with large, intricate networked sensor systems in situations where there is limited expert understanding of the frequently changing real-world contexts. Here, we demonstrate the variety of opportunities that data-driven modeling presents, and how they have been already implemented in various real-world applications.

Application of Gated Recurrent Units for CT Trajectory Optimization

Recent advances in computed tomography (CT) imaging, especially with dual-robot systems, have introduced new challenges for scan trajectory optimization. This paper presents a novel approach using Gated Recurrent Units (GRUs) to optimize CT scan trajectories. Our approach exploits the flexibility of robotic CT systems to select projections that enhance image quality by improving resolution and contrast while reducing scan time. We focus on cone-beam CT and employ several projection-based metrics, including absorption, pixel intensities, contrast-to-noise ratio, and data completeness. The GRU network aims to minimize data redundancy and maximize completeness with a limited number of projections. We validate our method using simulated data of a test specimen, focusing on a specific voxel of interest. The results show that the GRU-optimized scan trajectories can outperform traditional circular CT trajectories in terms of image quality metrics. For the used specimen, SSIM improves from 0.38 to 0.49 and CNR increases from 6.97 to 9.08. This finding suggests that the application of GRU in CT scan trajectory optimization can lead to more efficient, cost-effective, and high-quality imaging solutions.

EAGLE: An Edge-Aware Gradient Localization Enhanced Loss for CT Image Reconstruction

Computed Tomography (CT) image reconstruction is crucial for accurate diagnosis and deep learning approaches have demonstrated significant potential in improving reconstruction quality. However, the choice of loss function profoundly affects the reconstructed images. Traditional mean squared error loss often produces blurry images lacking fine details, while alternatives designed to improve may introduce structural artifacts or other undesirable effects. To address these limitations, we propose Eagle-Loss, a novel loss function designed to enhance the visual quality of CT image reconstructions. Eagle-Loss applies spectral analysis of localized features within gradient changes to enhance sharpness and well-defined edges. We evaluated Eagle-Loss on two public datasets across low-dose CT reconstruction and CT field-of-view extension tasks. Our results show that Eagle-Loss consistently improves the visual quality of reconstructed images, surpassing state-of-the-art methods across various network architectures. Code and data are available at \url{https://github.com/sypsyp97/Eagle_Loss}.

Deep Learning Computed Tomography based on the Defrise and Clack Algorithm

This study presents a novel approach for reconstructing cone beam computed tomography (CBCT) for specific orbits using known operator learning. Unlike traditional methods, this technique employs a filtered backprojection type (FBP-type) algorithm, which integrates a unique, adaptive filtering process. This process involves a series of operations, including weightings, differentiations, the 2D Radon transform, and backprojection. The filter is designed for a specific orbit geometry and is obtained using a data-driven approach based on deep learning. The approach efficiently learns and optimizes the orbit-related component of the filter. The method has demonstrated its ability through experimentation by successfully learning parameters from circular orbit projection data. Subsequently, the optimized parameters are used to reconstruct images, resulting in outcomes that closely resemble the analytical solution. This demonstrates the potential of the method to learn appropriate parameters from any specific orbit projection data and achieve reconstruction. The algorithm has demonstrated improvement, particularly in enhancing reconstruction speed and reducing memory usage for handling specific orbit reconstruction.

Data-Driven Filter Design in FBP: Transforming CT Reconstruction with Trainable Fourier Series

In this study, we introduce a Fourier series-based trainable filter for computed tomography (CT) reconstruction within the filtered backprojection (FBP) framework. This method overcomes the limitation in noise reduction, inherent in conventional FBP methods, by optimizing Fourier series coefficients to construct the filter. This method enables robust performance across different resolution scales and maintains computational efficiency with minimal increment for the trainable parameters compared to other deep learning frameworks. Additionally, we propose Gaussian edge-enhanced (GEE) loss function that prioritizes the $L_1$ norm of high-frequency magnitudes, effectively countering the blurring problems prevalent in mean squared error (MSE) approaches. The model's foundation in the FBP algorithm ensures excellent interpretability, as it relies on a data-driven filter with all other parameters derived through rigorous mathematical procedures. Designed as a plug-and-play solution, our Fourier series-based filter can be easily integrated into existing CT reconstruction models, making it a versatile tool for a wide range of practical applications. Our research presents a robust and scalable method that expands the utility of FBP in both medical and scientific imaging.

A 2D Sinogram-Based Approach to Defect Localization in Computed Tomography

The rise of deep learning has introduced a transformative era in the field of image processing, particularly in the context of computed tomography. Deep learning has made a significant contribution to the field of industrial Computed Tomography. However, many defect detection algorithms are applied directly to the reconstructed domain, often disregarding the raw sensor data. This paper shifts the focus to the use of sinograms. Within this framework, we present a comprehensive three-step deep learning algorithm, designed to identify and analyze defects within objects without resorting to image reconstruction. These three steps are defect segmentation, mask isolation, and defect analysis. We use a U-Net-based architecture for defect segmentation. Our method achieves the Intersection over Union of 92.02% on our simulated data, with an average position error of 1.3 pixels for defect detection on a 512-pixel-wide detector.

A gradient-based approach to fast and accurate head motion compensation in cone-beam CT

Cone-beam computed tomography (CBCT) systems, with their portability, present a promising avenue for direct point-of-care medical imaging, particularly in critical scenarios such as acute stroke assessment. However, the integration of CBCT into clinical workflows faces challenges, primarily linked to long scan duration resulting in patient motion during scanning and leading to image quality degradation in the reconstructed volumes. This paper introduces a novel approach to CBCT motion estimation using a gradient-based optimization algorithm, which leverages generalized derivatives of the backprojection operator for cone-beam CT geometries. Building on that, a fully differentiable target function is formulated which grades the quality of the current motion estimate in reconstruction space. We drastically accelerate motion estimation yielding a 19-fold speed-up compared to existing methods. Additionally, we investigate the architecture of networks used for quality metric regression and propose predicting voxel-wise quality maps, favoring autoencoder-like architectures over contracting ones. This modification improves gradient flow, leading to more accurate motion estimation. The presented method is evaluated through realistic experiments on head anatomy. It achieves a reduction in reprojection error from an initial average of 3mm to 0.61mm after motion compensation and consistently demonstrates superior performance compared to existing approaches. The analytic Jacobian for the backprojection operation, which is at the core of the proposed method, is made publicly available. In summary, this paper contributes to the advancement of CBCT integration into clinical workflows by proposing a robust motion estimation approach that enhances efficiency and accuracy, addressing critical challenges in time-sensitive scenarios.

Task-based Generation of Optimized Projection Sets using Differentiable Ranking

We present a method for selecting valuable projections in computed tomography (CT) scans to enhance image reconstruction and diagnosis. The approach integrates two important factors, projection-based detectability and data completeness, into a single feed-forward neural network. The network evaluates the value of projections, processes them through a differentiable ranking function and makes the final selection using a straight-through estimator. Data completeness is ensured through the label provided during training. The approach eliminates the need for heuristically enforcing data completeness, which may exclude valuable projections. The method is evaluated on simulated data in a non-destructive testing scenario, where the aim is to maximize the reconstruction quality within a specified region of interest. We achieve comparable results to previous methods, laying the foundation for using reconstruction-based loss functions to learn the selection of projections.

Optimizing CT Scan Geometries With and Without Gradients

In computed tomography (CT), the projection geometry used for data acquisition needs to be known precisely to obtain a clear reconstructed image. Rigid patient motion is a cause for misalignment between measured data and employed geometry. Commonly, such motion is compensated by solving an optimization problem that, e.g., maximizes the quality of the reconstructed image with respect to the projection geometry. So far, gradient-free optimization algorithms have been utilized to find the solution for this problem. Here, we show that gradient-based optimization algorithms are a possible alternative and compare the performance to their gradient-free counterparts on a benchmark motion compensation problem. Gradient-based algorithms converge substantially faster while being comparable to gradient-free algorithms in terms of capture range and robustness to the number of free parameters. Hence, gradient-based optimization is a viable alternative for the given type of problems.