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.

Fiducial markers are commonly used in navigation assisted minimally invasive spine surgery (MISS) and they help transfer image coordinates into real world coordinates. In practice, these markers might be located outside the field-of-view (FOV), due to the limited detector sizes of C-arm cone-beam computed tomography (CBCT) systems used in intraoperative surgeries. As a consequence, reconstructed markers in CBCT volumes suffer from artifacts and have distorted shapes, which sets an obstacle for navigation. In this work, we propose two fiducial marker detection methods: direct detection from distorted markers (direct method) and detection after marker recovery (recovery method). For direct detection from distorted markers in reconstructed volumes, an efficient automatic marker detection method using two neural networks and a conventional circle detection algorithm is proposed. For marker recovery, a task-specific learning strategy is proposed to recover markers from severely truncated data. Afterwards, a conventional marker detection algorithm is applied for position detection. The two methods are evaluated on simulated data and real data, both achieving a marker registration error smaller than 0.2 mm. Our experiments demonstrate that the direct method is capable of detecting distorted markers accurately and the recovery method with task-specific learning has high robustness and generalizability on various data sets. In addition, the task-specific learning is able to reconstruct other structures of interest accurately, e.g. ribs for image-guided needle biopsy, from severely truncated data, which empowers CBCT systems with new potential applications.