用神经网络分解动态PET图像，提升重建清晰度与连续性。
Dynamic PET Image Reconstruction via Non-negative INR Factorization
- 基于非负隐式神经表示因子分解，将动态图像建模为时空连续函数。
- 在泊松噪声下重建效果优于现有方法，保留解剖细节与浓度变化。
- 适合需要高精度动态医学成像的研究者，尤其关注图像连续性与几何细节。
从含噪投影数据中重建动态正电子发射断层扫描（PET）图像是一项重要但具有挑战性的任务。本文提出一种无监督学习方法——非负隐式神经表示因子分解（NINRF），基于未知图像的低秩矩阵分解，利用神经网络同时表示系数和基函数。数学上证明，若一组动态PET图像满足广义非负低秩特性，则可分解为一组在时空域中连续变化的非负函数。该方法将经典的非负矩阵分解（NMF）扩展至连续函数空间，并采用隐式神经表示（INR）实现离散矩阵到连续函数的映射。通过最小化KL散度并引入系数与基函数的稀疏正则化，优化神经网络参数。在存在泊松噪声的动态PET重建任务中，大量实验表明该方法显著优于其他方法，同时生成物体的连续几何特征和区域浓度变化表示。
原文摘要 · Abstract (English)
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 (\texttt{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.
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