PIFON-EPT：基于物理信息傅里叶网络的磁共振电阻抗断层成像
PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks
AI总结：
提出PIFON-EPT，一种基于物理信息傅里叶网络的深度学习方法，利用含噪声和不完整的MR测量同时重建电阻抗和发射场，在3T和7T模拟实验中实现低误差重建，并扩展至广义亥姆霍兹方程以改善界面效果。
摘要：
我们提出了用于电阻抗断层成像（EPT）的物理信息傅里叶网络（PIFON-EPT），这是一种基于深度学习的新方法，利用含噪声和/或不完整的磁共振（MR）测量数据进行电阻抗（EP）重建。我们的方法利用亥姆霍兹方程来约束两个网络，分别负责发射场的去噪与补全，以及物体电阻抗的估计。我们将随机傅里叶特征映射嵌入到网络中，以高效学习发射场中编码的高频细节。我们通过多个在3特斯拉（T）和7特斯拉（T）磁共振成像下的模拟实验验证了PIFON-EPT的有效性，并表明我们的方法能够重建物理一致的电阻抗和发射场。具体而言，当仅使用含噪声测量场的20%作为输入时，PIFON-EPT重建的体模电阻抗误差≤5%，且去噪和补全的测量误差≤1%。此外，我们将PIFON-EPT推广到求解考虑非均匀介质间电阻抗梯度的广义亥姆霍兹方程，这在不明确知道边界条件的情况下，改善了不同材料界面处的重建结果。PIFON-EPT是首个能够从不完整的含噪声MR测量中同时重建电阻抗和发射场的方法，为EPT研究提供了新的机遇。
英文摘要：
We propose Physics-Informed Fourier Networks for Electrical Properties (EP) Tomography (PIFON-EPT), a novel deep learning-based method for EP reconstruction using noisy and/or incomplete magnetic resonance (MR) measurements. Our approach leverages the Helmholtz equation to constrain two networks, responsible for the denoising and completion of the transmit fields, and the estimation of the object's EP, respectively. We embed a random Fourier features mapping into our networks to enable efficient learning of high-frequency details encoded in the transmit fields. We demonstrated the efficacy of PIFON-EPT through several simulated experiments at 3 and 7 tesla (T) MR imaging, and showed that our method can reconstruct physically consistent EP and transmit fields. Specifically, when only $20\%$ of the noisy measured fields were used as inputs, PIFON-EPT reconstructed the EP of a phantom with $\leq 5\%$ error, and denoised and completed the measurements with $\leq 1\%$ error. Additionally, we adapted PIFON-EPT to solve the generalized Helmholtz equation that accounts for gradients of EP between inhomogeneities. This yielded improved results at interfaces between different materials without explicit knowledge of boundary conditions. PIFON-EPT is the first method that can simultaneously reconstruct EP and transmit fields from incomplete noisy MR measurements, providing new opportunities for EPT research.
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