Joint <inline-formula><tex-math notation="LaTeX">$\text{B}_{0}$</tex-math></inline-formula> and Image Reconstruction in Low-Field MRI by Physics-Informed Deep-Learning

Objective: We present a model-based image reconstruction approach based on unrolled neural networks which corrects for image distortion and noise in low-field (<inline-formula><tex-math notation="LaTeX">$B_{0} \sim$</tex-math></inline-formula> 50 mT) MRI. Methods: Utilising knowledge about the underlying physics, a novel network architecture (SH-Net) is introduced which involves the estimation of spherical harmonic coefficients to guarantee a spatially smooth field map estimate. The SH-Net is integrated in an end-to-end trainable model which jointly estimates the <inline-formula><tex-math notation="LaTeX">$B_{0}$</tex-math></inline-formula>-field map as well as the image. Experiments were conducted on retrospectively simulated low-field data of human knees. Results: We compare our model to different model-based approaches at distinct noise levels and various <inline-formula><tex-math notation="LaTeX">$B_{0}$</tex-math></inline-formula>-field distributions. Our results show that our physics-informed neural network approach outperforms the purely model-based methods by improving the PSNR up to 11.7% and the RMSE up to 86.3%. Conclusion: Our end-to-end trained model-based approach outperforms existing methods in reconstructing image and <inline-formula><tex-math notation="LaTeX">$B_{0}$</tex-math></inline-formula>-field maps in the low-field regime. Significance: low-field MRI is becoming increasingly more popular as it enables access to MR in challenging situations such as intensive care units or resource poor areas. Our method allows for fast and accurate image reconstruction in such low-field imaging with <inline-formula><tex-math notation="LaTeX">$B_{0}$</tex-math></inline-formula>-inhomogeneity compensation under a wide range of various environmental conditions.