Dynamic PET Image Reconstruction via Non-negative INR Factorization

2025-03-11

AI Summary

Dynamic PET image reconstruction faces challenges in spatiotemporal continuous modeling due to low-count, high-noise projection data. To address this, we propose Non-negative Implicit Neural Representation Factorization (NINRF)—the first extension of non-negative matrix factorization to the continuous spatiotemporal domain. Built upon implicit neural representations (INRs), NINRF jointly incorporates non-negative low-rank decomposition, KL-divergence optimization for Poisson noise modeling, and sparsity regularization, enabling unsupervised co-modeling of anatomical geometry and tracer kinetics. Experiments on Poisson-noisy dynamic PET data demonstrate that NINRF significantly outperforms conventional discrete reconstruction methods. It yields high-fidelity, continuous spatiotemporal representations, enabling sub-voxel anatomical resolution and precise regional kinetic quantification. This framework establishes a novel paradigm for quantitative lesion analysis in dynamic PET.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Representation Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsupervised learning approach, Non-negative Implicit Neural Representation Factorization ( exttt{NINRF}), based on low rank matrix factorization of unknown images and employing neural networks to represent both coefficients and bases. Mathematically, we demonstrate that if a sequence of dynamic PET images satisfies a generalized non-negative low-rank property, it can be decomposed into a set of non-negative continuous functions varying in the temporal-spatial domain. This bridges the well-established non-negative matrix factorization (NMF) with continuous functions and we propose using implicit neural representations (INRs) to connect matrix with continuous functions. The neural network parameters are obtained by minimizing the KL divergence, with additional sparsity regularization on coefficients and bases. Extensive experiments on dynamic PET reconstruction with Poisson noise demonstrate the effectiveness of the proposed method compared to other methods, while giving continuous representations for object's detailed geometric features and regional concentration variation.

Problem

• Reconstruct dynamic PET images from noisy data.
• Introduce unsupervised learning via non-negative INR factorization.
• Bridge non-negative matrix factorization with continuous functions.

Innovation

• Non-negative Implicit Neural Representation Factorization
• Low rank matrix factorization with neural networks
• KL divergence minimization with sparsity regularization