Adaptive Voxel-Weighted Loss Using L1 Norms in Deep Neural Networks for Detection and Segmentation of Prostate Cancer Lesions in PET/CT Images

Accurate automated detection of recurrent prostate cancer in PSMA PET/CT scans is challenging due to heterogeneous lesion size, activity, anatomical location, and intra- and inter-class imbalances. Conventional deep learning loss functions often produce suboptimal optimization, as gradients are dominated by easy background voxels or extreme outliers. To address this, we propose L1-weighted Dice Focal Loss (L1DFL), which harmonizes gradient magnitudes across voxels using L1 norms to adaptively weight samples based on classification difficulty, resulting in well-calibrated predictions with a bimodal separation between correct and incorrect predictions. We trained three 3D convolutional networks (Attention U-Net, SegResNet, U-Net) and a transformer-based UNETR model on 380 PSMA PET/CT scans. PET and CT volumes were concatenated as input to the models. We also fine-tuned SAM-Med3D foundation model with the different loss functions and evaluated their performance. Across architectures, L1DFL consistently outperformed Dice Loss (DL) and Dice Focal Loss (DFL), achieving at least a 4% improvement in Dice Similarity Coefficient. F1 scores were higher by 6% and 26% compared to DL and DFL, respectively. While DFL produced more false positives and DL struggled with larger lesions, L1DFL achieved balanced detection, minimizing false detections while maintaining high true positive rates. The gradient harmonization mechanism ensured robustness across varying lesion sizes, volumes, and spread. The code is publicly available at: https://github.com/ObedDzik/pca_segment.git.