FourierPET: Deep Fourier-based Unrolled Network for Low-count PET Reconstruction

2026-01-16

AI Summary

This work addresses the severe image degradation in low-count PET reconstruction caused by Poisson noise, photon scarcity, and attenuation correction errors. The authors propose a Fourier-domain unfolding reconstruction framework optimized via ADMM, which for the first time reveals the separability of PET degradation factors in the frequency domain. Leveraging this insight, they design an amplitude–phase decoupled correction mechanism, integrating spectral consistency constraints with dual refinement modules to enable frequency-aware reconstruction. The method effectively suppresses high-frequency phase perturbations and low-frequency amplitude attenuation, achieving superior reconstruction quality, faster convergence, and enhanced model interpretability—all while significantly reducing the number of parameters.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Low-count positron emission tomography (PET) reconstruction is a challenging inverse problem due to severe degradations arising from Poisson noise, photon scarcity, and attenuation correction errors. Existing deep learning methods typically address these in the spatial domain with an undifferentiated optimization objective, making it difficult to disentangle overlapping artifacts and limiting correction effectiveness. In this work, we perform a Fourier-domain analysis and reveal that these degradations are spectrally separable: Poisson noise and photon scarcity cause high-frequency phase perturbations, while attenuation errors suppress low-frequency amplitude components. Leveraging this insight, we propose FourierPET, a Fourier-based unrolled reconstruction framework grounded in the Alternating Direction Method of Multipliers. It consists of three tailored modules: a spectral consistency module that enforces global frequency alignment to maintain data fidelity, an amplitude-phase correction module that decouples and compensates for high-frequency phase distortions and low-frequency amplitude suppression, and a dual adjustment module that accelerates convergence during iterative reconstruction. Extensive experiments demonstrate that FourierPET achieves state-of-the-art performance with significantly fewer parameters, while offering enhanced interpretability through frequency-aware correction.

Problem

• low-count PET reconstruction
• Poisson noise
• photon scarcity
• attenuation correction errors
• image degradation

Innovation

• Fourier-domain analysis
• unrolled network
• amplitude-phase decoupling
• low-count PET reconstruction
• ADMM