Physics informed neural network (PINN) for noise-robust phase-based magnetic resonance electrical properties tomography

Electrical properties could become a source of contrast for non-calcified tumor tissues. Magnetic Resonance Electrical Property Tomography (MREPT) relies on numerical differentiation to solve the partial differential equations (PDEs) to reconstruct electrical properties. However, the numerical differentiation for derivatives produces artifacts near tissue edges and amplifies noise. In this work, Physics-informed neural networks (PINNs), are employed to estimate derivatives for MREPT with automatic differentiation enabled by neural networks to improve noise robustness and reduce edge artifacts. PINNs require the balance of various loss functions and information from collocation points of ground truth and image boundary to learn to estimate the derivatives. In this work, a warm-up mechanism is used to reduce the complexity of the multiple loss balance. Results showed that even with only three collocation points and boundary conditions, reconstructions can be made from noise-contaminated source images (SNR 50). This proves that PINNs achieved noise-robust estimate of partial derivatives, thus leding to noise-robust conductivity reconstruction.