Physics-encoded Neural Network for the correction of encoding magnetic field in a low-field gradient-coil-free permanent magnet MRI system

Motivation: Using permanent magnets for polarization and encoding in a low-field body-part dedicated MRI enhances its portability and lowers the cost. However, the spatial encoding magnetic field decays over time which degrades image quality. Goal(s): AI-based correction of the decay without labor-intensive mapping of the magnetic field or additional hardware. Approach: Physics-encoded Neural Network (PeNN), which contains a model-based image reconstruction concept, is proposed to correct the decay. The gradients for the encoded physics are computed algorithmically instead of mathematically for backpropagation. Results: PeNN can model the decay accurately, leading to a 78% improvement of structural similarity index measure in both simulations and experiments. Impact: PeNN effectively and efficiently corrects the spatial encoding magnetic field in a portable MRI system using model-based imaging, saving regular labor-intensive mapping of magnetic fields. The proposed PeNN does not necessarily require the physics concept to be differentiable for backpropagation.