Unsupervised Adaptation from FDG to PSMA PET/CT for 3D Lesion Detection under Label Shift

1. Problem Statement

The paper addresses the challenge of Unsupervised Domain Adaptation (UDA) in 3D volumetric lesion detection for PET/CT imaging. Specifically, it aims to transfer a lesion detection model trained on labeled FDG-PET/CT data (source domain) to unlabeled PSMA-PET/CT data (target domain).

• The Core Challenge: While standard UDA methods often assume only covariate shift (differences in input appearance, e.g., tracer uptake patterns), this task suffers from significant label shift.
  • Lesion Characteristics: PSMA scans typically contain more numerous, smaller lesions compared to FDG scans, which tend to have fewer but larger lesions.
  • Prevalence: The number of lesions per subject differs significantly between the two tracers.
• Limitation of Existing Methods: Conventional UDA approaches (e.g., adversarial training or fixed-threshold self-training) fail because they assume the label distribution (size and count of lesions) remains consistent across domains. Applying a model trained on FDG directly to PSMA leads to poor detection of small lesions and incorrect lesion counts.

2. Methodology

The authors propose a Self-Training UDA Framework that explicitly models and compensates for label shift using two primary mechanisms: Adaptive Anchor Shapes and Prior-Guided Pseudo-Label Selection.

A. Backbone Architecture

• Model: Multimodal 3D RetinaNet (M3DRetinaNet), a one-stage object detector.
• Input: Stacked PET and CT volumes (dual-modality).
• Features: Utilizes a 3D ResNet backbone and a 3D Feature Pyramid Network (FPN) to handle multi-scale object sizes.
• Loss Function: Focal loss for classification and Smooth-L1 loss for box regression.

B. Mechanism 1: Epoch-wise Anchor Size Adaptation

Standard detectors use fixed anchor box shapes. If these shapes do not match the target domain's lesion sizes, regression errors increase.

• Strategy: The system adaptively adjusts anchor shapes based on the target domain's estimated lesion sizes.
• Process:
  1. Select high-confidence pseudo-labels from the target domain.
  2. Run k-means clustering on the volumes of these selected pseudo-boxes to estimate new centroid sizes.
  3. Update the anchor set using an Exponential Moving Average (EMA) to ensure stability:
     $$s^{(r)}_k \leftarrow (1 - \beta)s^{(r-1)}_k + \beta \tilde{s}^{(r)}_k$$
  • Result: This increases positive anchor coverage for the smaller lesions prevalent in PSMA data.

C. Mechanism 2: Prior-Guided Pseudo-Label Selection

Instead of using a fixed confidence threshold or selecting the top $N\%$ of predictions (which biases toward large, high-contrast lesions), the authors introduce a size-bin-wise quota system.

• Target Distribution Estimation:
  • Global Mean ($\mu$): Estimates the average number of lesions per subject in the target domain.
  • Size Histogram ($h$): Estimates the distribution of lesion volumes across $B$ bins (e.g., 10 volume bins).
  • Both are updated via EMA during training.
• Selection Algorithm:
  1. Per-Subject Budget: Calculate the allowed number of pseudo-labels for a subject based on the estimated mean $\mu$ and a scaling factor $\lambda$.
  2. Bin-wise Allocation: Distribute this budget across size bins according to the estimated histogram $h$.
  3. Selection: Within each size bin, sort candidates by confidence and retain the top $n_b$ candidates (where $n_b$ is the allocated quota for that bin).
• Result: This forces the model to select pseudo-labels that reflect the true size and count distribution of the PSMA domain, rather than inheriting the FDG bias.

D. Alternating Optimization

The training loop alternates between:

1. Supervised Learning: Training on labeled FDG source data.
2. Self-Training: Inferring on unlabeled PSMA data, updating the priors ($\mu, h$) and anchors ($S$), generating refined pseudo-labels, and training on these pseudo-labels.

• Note: The method avoids adversarial loss or explicit feature alignment, making it computationally efficient for 3D data.

3. Key Contributions

1. First 3D UDA for Lesion Detection: This is the first work to apply unsupervised domain adaptation specifically to 3D volumetric lesion detection in PET/CT.
2. Label Shift Mitigation: It introduces a novel self-training scheme that explicitly addresses label shift (differences in lesion size and count), a factor previously ignored in UDA detection tasks.
3. Adaptive Pseudo-Labeling: The development of a dynamic, bin-wise pseudo-label selection strategy driven by estimated target domain priors (size distribution and prevalence).
4. Anchor Adaptation: A method to dynamically update anchor box scales based on target domain statistics to improve regression stability for small lesions.

4. Experimental Results

The method was evaluated on the AutoPET 2024 dataset:

• Source: 501 labeled FDG studies.
• Target: 369 unlabeled PSMA studies (258 for training, 74 for testing).
• Metrics: Average Precision (AP) at IoU thresholds (0.1, 0.25, 0.5) and Free-Response ROC (FROC).

Performance Highlights:

• Source-Only Baseline: AP@0.1 = 0.225 (Poor performance due to domain shift).
• Conventional Self-Training: Improved AP but still biased toward larger lesions.
• Proposed Method (Full UDA + Label Shift):
  • AP@0.1: 0.613 (vs. 0.225 baseline).
  • AP@0.5: 0.417.
  • FROC: Showed significantly higher sensitivity for any given false-positive rate compared to baselines.
• Comparison: While the proposed method (0.613 AP@0.1) did not reach the "upper bound" of a model fine-tuned on labeled PSMA (0.729), it drastically outperformed the source-only model and standard self-training, proving the efficacy of modeling label shift.

5. Significance and Conclusion

• Clinical Impact: The framework enables the deployment of robust lesion detection models for new tracers (like PSMA) without the need for expensive, time-consuming manual annotations.
• Technical Insight: The paper demonstrates that in medical imaging, label shift (changes in disease prevalence and morphology) is as critical as covariate shift (changes in image appearance). Ignoring label shift leads to systematic under-detection of small lesions.
• Efficiency: The approach is lightweight, avoiding the computational burden of adversarial training in 3D, making it practical for clinical deployment.
• Future Work: The authors suggest extending the method to multi-class settings and incorporating uncertainty-weighted selection to handle clustered lesions better.

In summary, this work provides a robust, efficient, and state-of-the-art solution for cross-tracer PET/CT lesion detection by explicitly modeling and correcting for the statistical differences in lesion size and prevalence between domains.