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Tagged magnetic resonance imaging~(MRI) has been used for decades to observeand quantify the detailed motion of deforming tissue. However, this techniquefaces several challenges such as tag fading, large motion, long computationtimes, and difficulties in obtaining diffeomorphic incompressible flow fields.To address these issues, this paper presents a novel unsupervised phase-based3D motion estimation technique for tagged MRI. We introduce two keyinnovations. First, we apply a sinusoidal transformation to the harmonic phaseinput, which enables end-to-end training and avoids the need for phaseinterpolation. Second, we propose a Jacobian determinant-based learningobjective to encourage incompressible flow fields for deforming biologicaltissues. Our method efficiently estimates 3D motion fields that are accurate,dense, and approximately diffeomorphic and incompressible. The efficacy of themethod is assessed using human tongue motion during speech, and includes bothhealthy controls and patients that have undergone glossectomy. We show that themethod outperforms existing approaches, and also exhibits improvements inspeed, robustness to tag fading, and large tongue motion. The code isavailable: https://github.com/jasonbian97/DRIMET-tagged-MRI

DRIMET: Deep Registration for 3D Incompressible Motion Estimation in Tagged-MRI with Application to the Tongue