Robustness and Stability Analysis of Differentiable Shift-Variant FBP for Cone-Beam CT under Challenging Acquisition Settings

Technical Summary: Robustness and Stability Analysis of Differentiable Shift-Variant FBP for Cone-Beam CT

Problem Statement
Cone-beam computed tomography (CBCT) is widely used in image-guided interventions, yet maintaining high image quality under non-standard acquisition settings remains challenging. While the Feldkamp-Davis-Kress (FDK) algorithm offers computational efficiency, it assumes a circular orbit and degrades significantly when applied to non-circular or irregular trajectories common in robotic C-arm systems. Conversely, model-based iterative reconstruction (MBIR) methods can handle general trajectories but suffer from high computational costs and complex regularization requirements. Previous work introduced a differentiable shift-variant filtered backprojection (SV-FBP) framework that learns redundancy weights in a data-driven manner, removing the need for analytically derived weights dependent on trajectory derivatives. However, the robustness of this framework under highly irregular, discontinuous, and sparse-view conditions, as well as its applicability to multi-isocenter geometries, required systematic evaluation.

Methodology
The study retains the core differentiable SV-FBP architecture based on Known Operator Learning. In this framework, the reconstruction pipeline is reformulated as a neural network where analytical operators (2D Radon transform, differentiation, backprojection) are explicitly retained, and only the trajectory-dependent redundancy weights are learned from data. This approach preserves interpretability while enabling adaptation to arbitrary source trajectories.

The evaluation was conducted using a simulated clinical Artis zeego C-arm CT geometry with three distinct experimental directions:

1. Discontinuous Trajectories: The framework was tested on three fixed-isocenter trajectory classes: Random Trajectory (RT), Random Nearest-Neighbor Reordered (RNNR), and Random Farthest-Neighbor Reordered (RFNR). These were designed to test sensitivity to trajectory ordering and continuity, ranging from fully random to maximally discontinuous jumps.
2. Sparse-View Reconstruction: Performance was evaluated under varying projection densities (400, 300, 200, and 100 views) to identify the limits of the method compared to an algebraic iterative reconstruction (AIR) baseline.
3. Multi-Isocenter Geometry: The framework was applied to a Lissajous-saddle trajectory where the rotation center varies continuously throughout the scan, testing applicability beyond fixed-isocenter assumptions.

Training utilized synthetic ground-truth volumes with geometric primitives, while inference included both synthetic and real-patient data from the Pancreatic-CT-CBCT-SEG dataset. The model was optimized using a combined MSE and SSIM loss function.

Key Contributions

• Systematic Robustness Analysis: The study provides a comprehensive assessment of differentiable SV-FBP under aggressive discontinuities (RFNR), demonstrating that the framework remains stable despite severe trajectory irregularities.
• Identification of Performance Drivers: The analysis reveals that reconstruction quality is governed primarily by the spatial distribution of sampling points rather than the continuity or ordering of the trajectory.
• Sparse-View Transition Regime: The paper identifies a clear transition regime where the method remains competitive with iterative approaches at moderate sampling densities (300–400 views) but degrades under severe undersampling (100–200 views) due to the lack of iterative data consistency.
• Multi-Isocenter Applicability: The framework is shown to function effectively on non-planar, multi-isocenter trajectories (Lissajous-saddle) without requiring architectural modifications.

Results

• Trajectory Robustness: Quantitative metrics (MSE, PSNR, SSIM) across RT, RNNR, and RFNR trajectories were highly consistent. Visualizations confirmed that reconstruction quality did not significantly degrade with increased discontinuity. Learned redundancy weights exhibited similar spatial patterns across all trajectory types after aligning source-position indexing, indicating that the model adapts to the spatial distribution of samples rather than the traversal order.
• Sparse-View Performance: At moderate sampling (300–400 views), differentiable SV-FBP achieved reconstruction quality comparable to or slightly better than 50-iteration AIR, with a computation time reduction of approximately one order of magnitude. Under severe undersampling (100–200 views), the iterative baseline outperformed SV-FBP, as AIR's iterative updates partially compensated for inconsistent measurements, whereas the FBP-type pipeline of SV-FBP could not.
• Multi-Isocenter Evaluation: On the Lissajous-saddle trajectory, the framework achieved metrics (MSE: 0.0984, PSNR: 36.41 dB, SSIM: 0.9521) comparable to fixed-isocenter sinusoidal trajectories, successfully reconstructing fine structural details with limited artifacts.

Significance and Claims
The paper positions differentiable SV-FBP as a flexible and efficient solution for non-standard and robotic CBCT acquisition scenarios. The findings clarify that the method is robust to strong trajectory irregularity, making it suitable for complex robotic paths where analytical weighting schemes fail. However, the authors modestly note that the method's limitations emerge under severe undersampling, where the absence of iterative data consistency leads to performance degradation relative to iterative baselines. Consequently, the framework is presented as a practical compromise between the speed of analytical reconstruction and the flexibility of data-driven weighting, offering a viable alternative for clinical applications where acquisition trajectories deviate from standard circular designs but where sampling density remains moderate. Future work is suggested to combine this framework with explicit data-consistency mechanisms to address severe undersampling.