Solving a Nonlinear Blind Inverse Problem for Tagged MRI with Physics and Deep Generative Priors

Zhangxing Bian; Shuwen Wei; Samuel W. Remedios; Junyu Chen; Aaron Carass; Blake E. Dewey; Jerry L. Prince

eess.IVMar 1, 2026

Solving a Nonlinear Blind Inverse Problem for Tagged MRI with Physics and Deep Generative Priors

Authors: Zhangxing Bian, Shuwen Wei, Samuel W. Remedios, Junyu Chen, Aaron Carass, Blake E. Dewey, Jerry L. Prince

Organizations: Johns Hopkins University · Johns Hopkins School of Medicine

Abstract

Tagged MRI enables tracking internal tissue motion non-invasively. It encodes motion by modulating anatomy with periodic tags, which deform along with tissue. However, the entanglement between anatomy, tags and motion poses significant challenges for post-processing. The existence of tags and imaging blur hinders downstream tasks such as segmenting anatomy. Tag fading, due to T1-relaxation, disrupts the brightness constancy assumption for motion tracking. For decades, these challenges have been handled in isolation and sub-optimally. In contrast, we introduce a blind and nonlinear inverse framework for tagged MRI that, for the first time, unifies these tasks: anatomical image recovery, high-resolution cine image synthesis, and motion estimation. At its core, the synergy of MR physics and generative priors enables us to blindly estimate the unknown forward imaging models and high-resolution underlying anatomy, while simultaneously tracking 3D diffeomorphic Lagrangian motion over time. Experiments on tagged brain MRI demonstrate that our approach yields high-resolution anatomy images, cine images, and more accurate motion than specialized methods.

Figures & tables

Figure 2: Qualitative comparison of tag-to-cine synthesis. For two subjects, we show early ( $t{=}1$ ) and late ( $t{=}6$ ) frames. Left-most column shows input tagged MRI (other views and orientations are omitted) while right-most shows ground-truth cine. Fourier spectrum of input and ours are shown. Orange arrows indicate the faded and smeared harmonic peaks. Red arrows indicate the aliasing artifact.

Methods	Timeframe	PSNR $\uparrow$	SSIM $\uparrow$
LowpassFuse	$t{=}1$	26.43 $\pm$ 1.40	0.62 $\pm$ 0.06
	$t{=}6$	26.68 $\pm$ 1.39	0.66 $\pm$ 0.05
HARP Demod.	$t{=}1$	24.28 $\pm$ 1.26	0.52 $\pm$ 0.04
	$t{=}6$	23.93 $\pm$ 1.17	0.54 $\pm$ 0.03
Ours	$t{=}1$	28.38 $\pm$ 1.41	0.83 $\pm$ 0.04
	$t{=}6$	28.41 $\pm$ 1.36	0.84 $\pm$ 0.03

Table 1: Quantitative comparison of tagged-to-cine synthesis across methods and timeframes, reported as mean

\pm

std.

Figure 3: Results of estimated point spread functions (PSFs) under different blurring settings and noise levels.

Figure 4: Motion magnitude comparison across methods. Cols. 1-2: input tagged MRI at two time points. Last column: ground-truth motion magnitude. Both sagittal and coronal views are shown.

Figure 5: Real tagged MRI: gel cylinder.

Method	Opt.	EPE $\downarrow$	EPE@95 $\downarrow$	NegDet(%) $\downarrow$
LKUnet [ 25 ]	✗	1.35 $\pm$ 0.65	2.94 $\pm$ 1.30	0.043
DeepTag [ 62 ]	✗	1.27 $\pm$ 0.58	2.97 $\pm$ 1.13	0.060
SyN [ 4 ]	✓	1.06 $\pm$ 0.31	2.41 $\pm$ 0.80	$<0.001$
DRIMET [ 12 ]	✓	0.79 $\pm$ 0.14	1.61 $\pm$ 0.53	$<0.001$
Ours	✓	0.60 $\pm$ 0.11	1.31 $\pm$ 0.22	$<0.001$

Table 3: Quantitative comparison of motion estimation accuracy. “Opt.” denotes whether the method is optimization-based.

PSF Params		Tag Params		Metrics
$\gamma_{\perp}$	$0.42\pm 0.03$	$\alpha_{1}$	$0.74\pm 0.09$	PSNR	$28.14\pm 0.11$
$\gamma_{\parallel}$	$1.03\pm 0.06$	$\alpha_{2}$	$10.1\pm 0.00$	SSIM	$0.81\pm 0.02$
$\gamma_{\text{thru}}$	$2.95\pm 0.12$	$\alpha_{3}$	$-1.14\pm 0.00$	EPE	$0.63\pm\mathbf{0.03}$
		$\alpha_{4}$	$0.22\pm 0.07$

Table 5: Empirical identifiability analysis. Mean

\pm

standard deviation across

N{=}5

independent runs with random initializations.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Data fidelity vs. prior strength. A sweep from strong prior ( $\rho^{*}=1$ ) to strong data fidelity ( $\rho^{*}=200$ ).

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Magnetic resonance imaging (MRI) is highly susceptible to patient motion due to its relatively long acquisition times and the fact that data are acquired sequentially in k-space. Even small patient movements introduce phase inconsistencies across measurements, leading to severe artifacts such as blurring, ghosting, and geometric distortions that can compromise diagnostic quality. Retrospective motion compensation remains challenging, particularly in accelerated acquisitions, due to the ill-posed nature of the joint reconstruction and motion estimation problem. In this work, we propose a unified Bayesian framework for motion-compensated 3D MRI that jointly estimates the anatomical image, rigid-body motion parameters, and coil sensitivity maps directly from motion-corrupted k-space data. Our approach integrates pretrained 3D complex-valued score-based diffusion models as expressive anatomical image priors within a physics-based forward model. Inference is performed by alternating diffusion posterior image updates with efficient proximal optimization steps for motion and coil sensitivity estimation, enabling fully unsupervised reconstruction without the need for paired motion-free training data. Experiments on simulated and real-motion brain MRI datasets demonstrate that the proposed method achieves improved image quality and motion robustness compared to state-of-the-art classical and learning-based motion correction techniques, particularly in the presence of severe motion and high acceleration.

Abstract

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