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

arXiv: https://arxiv.org/abs/2601.11680 · HTML: https://mlsanity.com/paper/2601.11680/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 16 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [DarkIR: Robust Low-Light Image Restoration](https://mlsanity.com/paper/2412.13443/) (2024)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [M3Net: Multi-view Encoding, Matching, and Fusion for Few-shot Fine-grained Action Recognition](https://mlsanity.com/paper/2308.03063/) (2023)
- [FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining](https://mlsanity.com/paper/2405.19450/) (2024)
- [UnfoldIR: Rethinking Deep Unfolding Network in Illumination Degradation Image Restoration](https://mlsanity.com/paper/2505.06683/) (2025)
- [Contrastive Diffusion Model with Auxiliary Guidance for Coarse-to-Fine PET Reconstruction](https://mlsanity.com/paper/2308.10157/) (2023)
- [Seeing the Unseen: A Frequency Prompt Guided Transformer for Image Restoration](https://mlsanity.com/paper/2404.00288/) (2024)
- [EfficientViM: Efficient Vision Mamba with Hidden State Mixer based State Space Duality](https://mlsanity.com/paper/2411.15241/) (2024)
- [RED: Residual Estimation Diffusion for Low-Dose PET Sinogram Reconstruction](https://mlsanity.com/paper/2411.05354/) (2024)

## Built on by (most cited first, 1 of 1)

- [FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction](https://mlsanity.com/paper/2607.11104/) (2026)

## Abstract (arXiv)

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.