Technical Summary: Neighbor2Inverse for Low-Dose PBI-CT Denoising

Problem Statement

Propagation-based X-ray phase-contrast imaging (PBI) offers superior soft-tissue contrast, particularly for lung imaging, potentially reducing the need for invasive biopsies. However, translating PBI to clinical practice requires significant radiation dose reduction. Current strategies to lower dose—such as reducing exposure time, limiting projections, or restricting the field of view to a Region of Interest (ROI)—inevitably increase image noise and introduce artifacts (e.g., truncation artifacts, ring artifacts).

While deep learning-based denoising has shown promise, supervised methods require paired low-dose and high-dose datasets, which are rarely available in practice due to ethical and logistical constraints. Simulated data often fails to replicate real-world noise characteristics, introducing bias. Existing self-supervised methods (e.g., Noise2Noise, Neighbor2Neighbor, Noise2Inverse) address the lack of ground truth but are not well-adapted to the specific challenges of ROI PBI-CT, which include spatially correlated noise, phase retrieval requirements, and high computational demands from large pixel counts.

Methodology

The authors propose Neighbor2Inverse, a self-supervised denoising framework designed specifically for low-dose PBI-CT that generalizes to clinical CT. The method adapts the Neighbor2Neighbor principle to the tomographic inverse problem.

Core Pipeline

1. Subsampling in Projection Domain: Instead of subsampling the reconstructed image, the method subsamples the raw projection data ($p_\phi$). A single noisy projection is divided into non-overlapping $2 \times 2$ pixel patches. From each patch, two neighboring pixels are randomly selected to generate two subsampled variants, $g_1(p_\phi)$ and $g_2(p_\phi)$. These variants share nearly identical structural information but contain statistically independent noise realizations.
2. Reconstruction Pipeline: The subsampled projections undergo the standard PBI reconstruction pipeline:
   • Phase Retrieval: Thickness maps are computed using the single-material phase retrieval algorithm (Paganin et al.).
   • Reconstruction: Filtered Backprojection (FBP) is applied to generate image slices.
3. Training Objective: A U-Net denoising network ($f_\theta$) is trained in the image domain. One reconstructed slice (derived from $g_1$) is fed into the network, and the other (derived from $g_2$) serves as the target. The network learns to map the noisy input to the "cleaner" target without requiring a noise-free ground truth.
4. Loss Functions:
   • Base Loss ($L_{Nei}$): Minimizes the difference between the network output and the target subsampled reconstruction.
   • Regularization ($L_{reg}$): An adaptation of the Neighbor2Neighbor correction term to account for potential signal discrepancies between the subsampled inputs.
   • Data Fidelity Variants: The authors also explored replacing $L_{reg}$ with data fidelity terms ($L_{origSino}$ and $L_{virtSino}$), which compare the network output (after forward projection) against the original or virtual sinograms to enforce consistency with the measured data.

Experimental Setup

• PBI Dataset: Calf lung scans acquired at the Australian Synchrotron. Data includes 3600 projections at 70 keV. Seven exposure times (15ms to 200ms) were tested. The 200ms scans served as high-quality references, while 15ms scans simulated low-dose conditions.
• Clinical Dataset: 200 chest CT exams from the RSNA Pulmonary Embolism Detection Challenge. Low-dose conditions were simulated by forward-projecting volumes and adding mixed Poisson-Gaussian noise.
• Comparisons: The method was benchmarked against analytical filters (Gaussian, BM3D, TV, Wavelet), other self-supervised methods (Noise2Inverse, Neighbor2Neighbor, Blind2Unblind, Proj2Proj, ZeroShotN2N, Filter2Noise, SDCNN), and a supervised approach using synthetic noise (FakeNoiseNet).

Key Contributions

1. Novel Framework: Introduction of Neighbor2Inverse, the first self-supervised denoising method tailored specifically for the inverse problem of ROI PBI-CT, addressing spatially correlated noise and phase retrieval constraints.
2. Domain Adaptation: The method successfully bridges the gap between projection-domain subsampling and image-domain denoising, allowing the network to exploit spatial correlations in the final reconstructed images.
3. Comprehensive Evaluation: A systematic comparison against a broad range of analytical and learning-based methods on both synchrotron PBI data and simulated clinical CT data.
4. Robustness Analysis: Investigation of the method's performance under sparse-view conditions (undersampling) and sensitivity to regularization hyperparameters.

Results

• PBI Data (15ms vs. 200ms): Neighbor2Inverse achieved superior noise suppression while preserving fine structural details (e.g., alveolar boundaries) compared to analytical methods and other self-supervised approaches.
  • Metrics: It achieved the highest composite image quality index ($Q = \text{CNR}/\text{SR}$) among all tested methods. Specifically, the sinogram subsampling variant achieved a $Q$ of $2.507 \pm 1.087$, outperforming the 200ms reference ($1.413 \pm 0.304$) in this metric.
  • Visuals: Unlike methods that oversmooth (e.g., TV, Gaussian) or introduce structural distortions (e.g., FakeNoiseNet), Neighbor2Inverse maintained sharpness and reduced noise effectively.
• Clinical Data: On simulated low-dose clinical CT, Neighbor2Inverse demonstrated competitive performance, closely matching the supervised U-Net in PSNR and SSIM, though Noise2Inverse showed slightly higher scores on these specific metrics (which the authors note favor over-smoothed images).
• Sparse-View Performance: When applied to data with only 900 projections (half the original), Neighbor2Inverse reduced both noise and angular undersampling artifacts, though with some attenuation of contrast in fine structures.
• Dose Reduction Strategy: The study found that reducing exposure time per projection is less detrimental to image quality than reducing the number of projections, as the thickness retrieval step acts as an implicit noise filter.

Significance and Claims

The paper claims that Neighbor2Inverse represents a significant step toward the clinical translation of PBI by enabling high-quality imaging at substantially reduced radiation doses without the need for paired high-dose training data.

• Clinical Relevance: The method addresses the critical barrier of radiation safety in lung imaging, potentially reducing the need for invasive biopsies by providing sufficient diagnostic detail non-invasively.
• Methodological Insight: The authors demonstrate that for this specific application, data regularization (via $L_{reg}$) is not strictly essential for effective training, though data fidelity terms can improve structural preservation at the cost of slightly higher residual noise.
• Limitations and Future Work: The authors modestly acknowledge that quantitative metrics (CNR, SSIM, PSNR) can be insensitive to subtle structural distortions and may favor over-smoothed images. They suggest that future work should focus on task-based evaluation to better align with clinical diagnostic needs. Additionally, a more thorough investigation of data-fidelity formulations is proposed as a promising direction.

The work concludes that Neighbor2Inverse consistently enhances image quality in low-dose regimes and remains robust under moderate undersampling, offering a viable pathway for bringing PBI closer to clinical application.