Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA PET Synthesis in Prostate Cancer

Deep learning models that synthesize PET from CT or MRI can reduce patient dose and scanner demand, but are typically optimized with global losses such as L1 or mean squared error (MSE) that treat all voxels similarly. In whole-body PSMA-PET, tumor voxels occupy only a small fraction of the volume, yet carry the clinically relevant activity signal; as a result, models can achieve high structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) while still underestimating lesion activity or failing to preserve tumor-specific structure. Radiomics provides biologically meaningful descriptors of tumor intensity and texture, but direct radiomics conditioning is time-consuming because it requires feature extraction from delineated lesion regions. We propose LAFNO, a Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA-PET synthesis that replaces high-dimensional radiomics conditioning with two efficient CT-derived proxy channels. Motivated by radiomics analysis of PSMA-avid tumor core and peritumoral regions, LAFNO uses a contrast proxy for local density variation and a disorder proxy for local texture heterogeneity, both injected into the model bottleneck. LAFNO combines whole-volume reconstruction with lesion-level total lesion activity (TLA), tumor-core contrast, and peritumoral supervision. We evaluated LAFNO against four baseline architectures on the TCIA PSMA-PET-CT-Lesions dataset. LAFNO remained competitive on whole-volume image quality, achieving SSIM of 0.960 and 0.938 for 18F- and 68Ga-PSMA, respectively, while reducing per-patient TLA error to 48.3% and 64.0% for 18F- and 68Ga-PSMA, respectively, and achieving the highest tumor-core radiomics reproducibility across all feature classes for both tracers. Peritumoral reproducibility remained tracer-dependent, indicating that biological fidelity in synthetic PSMA-PET remains challenging.