PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks
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Objective: In this paper, we introduce Physics-Informed Fourier Networks (PIFONs) for Electrical Properties (EP) Tomography (EPT). Our novel deep learning-based method is capable of learning EPs globally by solving an inverse scattering problem based on noisy and/or incomplete magnetic resonance (MR) measurements. Methods: We use two separate fully-connected neural networks, namely B_1^+ Net and EP Net, to learn the B_1^+ field and EPs at any location. A random Fourier features mapping is embedded into B_1^+ Net, which allows it to learn the B_1^+ field more efficiently. These two neural networks are trained jointly by minimizing the combination of a physics-informed loss and a data mismatch loss via gradient descent. Results: We showed that PIFON-EPT could provide physically consistent reconstructions of EPs and transmit field in the whole domain of interest even when half of the noisy MR measurements of the entire volume was missing. The average error was 2.49%, 4.09% and 0.32% for the relative permittivity, conductivity and B_1^+, respectively, over the entire volume of the phantom. In experiments that admitted a zero assumption of B_z, PIFON-EPT could yield accurate EP predictions near the interface between regions of different EP values without requiring any boundary conditions. Conclusion: This work demonstrated the feasibility of PIFON-EPT, suggesting it could be an accurate and effective method for electrical properties estimation. Significance: PIFON-EPT can efficiently de-noise MR measurements, which shows the potential to improve other MR-based EPT techniques. Furthermore, it is the first time that MR-based EPT methods can reconstruct the EPs and B_1^+ field simultaneously from incomplete simulated noisy MR measurements.
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