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DEQ-MPI: A Deep Equilibrium Reconstruction with Learned Consistency for Magnetic Particle Imaging

Alper G\"ung\"orBaris AskinDamla Alptekin SoydanCan Bar{\i}\c{s} TopEmine Ulku SaritasTolga \c{C}ukur
Dec 2022
摘要
Magnetic particle imaging (MPI) offers unparalleled contrast and resolutionfor tracing magnetic nanoparticles. A common imaging procedure calibrates asystem matrix (SM) that is used to reconstruct data from subsequent scans. Theill-posed reconstruction problem can be solved by simultaneously enforcing dataconsistency based on the SM and regularizing the solution based on an imageprior. Traditional hand-crafted priors cannot capture the complex attributes ofMPI images, whereas recent MPI methods based on learned priors can suffer fromextensive inference times or limited generalization performance. Here, weintroduce a novel physics-driven method for MPI reconstruction based on a deepequilibrium model with learned data consistency (DEQ-MPI). DEQ-MPI reconstructsimages by augmenting neural networks into an iterative optimization, asinspired by unrolling methods in deep learning. Yet, conventional unrollingmethods are computationally restricted to few iterations resulting innon-convergent solutions, and they use hand-crafted consistency measures thatcan yield suboptimal capture of the data distribution. DEQ-MPI instead trainsan implicit mapping to maximize the quality of a convergent solution, and itincorporates a learned consistency measure to better account for the datadistribution. Demonstrations on simulated and experimental data indicate thatDEQ-MPI achieves superior image quality and competitive inference time tostate-of-the-art MPI reconstruction methods.
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