A Deep Equilibrium Technique for 3D MPI Reconstruction

Abstract

Image reconstruction in MPI involves estimation of the particle concentration given acquired data and system matrix (SM). As this is an ill-posed inverse problem, image quality depends heavily on prior information used to improve problem conditioning. Recent learning-based priors show great promise for MPI reconstruction, but priors purely driven by image samples in training datasets can show limited reliability and generalization. Here, we propose 3DEQ-MPI, a new deep equilibrium technique for 3D MPI reconstruction. 3DEQ-MPI is based on an infinitely-unrolled network architecture that synergistically leverages a data-driven prior to learn attributes of MPI images and a physics-driven prior to enforce fidelity to acquired data based on the SM. 3DEQ-MPI is trained on a simulated dataset, and unlike common deep equilibrium models, it utilizes a Jacobian-free backpropagation algorithm for fast and stable convergence. Demonstrations on simulated data and experimental OpenMPI data clearly show the superior performance of 3DEQ-MPI against competing methods.