LGGS: Longitudinal MRI Reconstruction via Guided Group Sparsity

Nikola Janjušević; Hersh Chandarana; Yao Wang; Li Feng

eess.IVOct 15, 2026

LGGS: Longitudinal MRI Reconstruction via Guided Group Sparsity

Authors: Nikola Janjušević, Hersh Chandarana, Yao Wang, Li Feng

Organizations: Radiology Department, New York University Grossman School of Medicine, New York, NY 10016 USA · Electrical and Computer Engineering Department, New York University Tandon School of Engineering, Brooklyn, NY 11201 USA

Abstract

Serial MRI is routinely performed in current clinical practice for disease surveillance and applications such as MR-guided radiotherapy. However, long MRI scan times increase costs and limit patient access, making accelerated image reconstruction of broad clinical importance. Previous scans of the same patient contain image information highly correlated with the current exam, yet existing reconstruction methods rarely exploit this information. Major challenges in the effective use of prior scans include inter-visit misregistration, pathological changes, and image phase variation. In this work, we propose Longitudinal Guided Group Sparsity (LGGS), an interpretable deep-learning framework for longitudinally informed MRI reconstruction derived from classical group sparsity. The prior scan is incorporated into the reconstruction regularizer through learned phase-invariant circulant attention that identifies corresponding features across exams. This formulation provides robustness to local in-plane and through-plane misregistration as well as inter-visit phase variation. Across acceleration rates, LGGS achieves state-of-the-art performance on longitudinal T1-weighted multi-coil brain MRI data, outperforming the evaluated unguided and longitudinally informed reconstruction methods, with substantially fewer learned parameters. We further evaluated the contributions of multiple guide slices and phase-invariant similarity and demonstrated that accelerated prior images can also serve as effective guides with minimal degradation in reconstruction quality.

Figures & tables

Fig. 1 : Longitudinal accelerated multi-coil MRI reconstruction. Images are shown as complex-valued, hue encoding phase (key, top right). (A) LGGS takes a prior visit acquired at $4\times$ as a guide for a current visit acquired at $12\times$ . (B) An unguided reconstruction of the same measurements discards it and fails to resolve pathology development (see zoom region). Patient image data is non-trivially related over visits due to image misregistration (in-plane and through-plane), disease progression, and inter-visit phase change. The issue of inter-visit phase remains even for methods using magnitude-based guidance as relative phase difference to the complex-valued reconstruction persists.

$\bm{x}\in\mathbb{C}^{NC}$	a vector-valued image with $N=N_{1}\times N_{2}$ pixels,
$\bm{x}\in\mathbb{C}^{NC}$	and vectorized channels, $\bm{x}=[\bm{x}_{1}^{\top},\,\cdots,\,\bm{x}_{C}^{\top}]^{\top}$ .
$\bm{x}_{c}\in\mathbb{C}^{N}$	the $c$ -th channel/coil of $\bm{x}$ .
$\bm{x}[n]\in\mathbb{C}^{C}$	the $n$ -th pixel of $\bm{x}$ , $n\in[1,\,N]$ .
$\bm{U}\otimes\bm{V}\in\mathbb{C}^{QM\times NC}$	Kronecker product of $\bm{U}\in\mathbb{C}^{Q\times N}$ and $\bm{V}\in\mathbb{C}^{M\times C}$ ,
$\bm{U}\otimes\bm{V}\in\mathbb{C}^{QM\times NC}$	i.e. the block matrix with $\bm{U}$ s scaled by $\bm{V}_{ij}~\forall~i,j$ .
$\bm{y}=\underline{\bm{U}}\bm{x}\equiv(\bm{U}\otimes\bm{I}_{C})\bm{x}$	the matrix $\bm{U}$ applied channel-wise,

TABLE I : Notation.

Fig. 2 : LGGS architecture.

K

unrolled primal–dual iterations ( 13 ). The guide image

\bm{w}

enters only through its analysis codes

\bm{v}

, which reach the dual update through the guided group-thresholding operator

\mathrm{GGT}_{\bm{\tau}}(\bm{z};\,\bm{v})

( 12 ), whose threshold is divided by the guided group energy map

\bm{\mathcal{E}}^{\alpha\beta}_{\bm{\Gamma}}(\bm{z};\,\bm{v})

( 11 ), in which the longitudinal adjacency

\bm{\Gamma}_{zv}

acts. The subtraction following

\mathrm{GGT}_{\bm{\tau}}

forms its Fenchel conjugate

\mathrm{GGT}^{\ast}_{\bm{\tau}}

. Setting

\bm{v}=0

recovers the unguided LPDSNet [ 9 ] exactly.

nominal rate $R$	$6\times$	$8\times$	$10\times$	$12\times$	$16\times$
center-fraction (%)	5.33	4.00	3.20	2.67	2.67
$R_{\mathrm{eff}}$	4.74	6.40	8.00	8.83	11.64

TABLE II : Uniform undersampling configuration. The fully sampled center shrinks with the nominal rate

R

until

{R=12}

Method	params	time (ms)
Method	params	forward	backward	total
E2EVarNet	$33.3$ M	$81$	$410$	$491$
LPDSNet	$1.00$ M	$85$	$155$	$241$
L-TGVN	$43.6$ M	$216$	$620$	$836$
LGGS	$1.08$ M	$234$	$547$	$780$
ESPIRiT	–	$166$	–	$166$

TABLE III : Learned parameter count, and wall-clock time of one forward and backward pass over a complete reconstruction on a single NVIDIA A100. ESPIRiT is coil-map estimation rather than a reconstruction method: it carries no learned parameters, is never backpropagated, and runs once per slice to build the forward operator given to LPDSNet and LGGS.

Fig. 3 : Reconstruction quality across effective acceleration rates (see Table II ) on the longitudinal brain dataset, for the unguided LPDSNet [ 9 ] and E2EVarNet [ 8 ] , the guided longitudinal L-TGVN [ 15 ] , and the proposed LGGS, over three metrics (NRMSE / SSIM / LPIPS).

Fig. 4 : Visual comparison, one case per row, each shown at its own acceleration rate. (A) Magnitude reconstructions of the target visit, with NRMSE / SSIM / LPIPS ( $\times 100$ ) above each panel. (B) Magnitude images of the prior visit supplied to the guided methods (3 slices), with residuals and metrics taken against the target visit at $\times 2$ gain. Slice $+0$ denotes the center guide slice for the corresponding target slice. Every panel within a row crops the same pixel window.

Fig. 5 : A single slice reconstructed across acceleration rates, with every panel cropped to the same window. NRMSE / SSIM / LPIPS ( $\times 100$ ) are given above each panel.

Fig. 6 : Ablation over the guide representation (complex-valued vs. magnitude) crossed with the feature similarity (distance vs. the phase-invariant distance of Section III-D ), at

8\times

nominal acceleration. Two marker sets are stacked above each bar:

\ast

tests against LGGS (gComplex, piDist),

\scriptstyle\square

against LGGS (gMag, piDist).

Fig. 7 : Ablation over the number of guide slices

N_{g}

8\times

nominal acceleration. Markers test against LGGS (

N_{g}=3

), the configuration used in every other figure.

Fig. 8 : Reconstruction quality when the guide is itself an accelerated reconstruction rather than a fully sampled prior (Section IV-E ).

Fig. S1 : The four guide (complex-valued vs. magnitude) and similarity (distance vs. the phase-invariant distance) combinations at $8\times$ nominal acceleration, on two cases. Panels are complex-valued with hue encoding phase; the magnified insets are magnitude. NRMSE / SSIM / LPIPS ( $\times 100$ ) are given above each panel.

Fig. S2 : Guide-slice ablation for a case of severe through-plane misregistration at $8\times$ . (A) reconstructions, unguided then $N_{g}=1,\,3,\,5$ ; (B) the guide slices those runs were given, the window centered on the co-located slice. Here slice $+1$ matches the target better than slice $+0$ ( $33.93$ % against $53.27$ % NRMSE), so widening the window keeps paying, from $9.65$ % at $N_{g}=3$ to $8.80$ % at $N_{g}=5$ . Figure S3 gives a mild case, in which $N_{g}=3$ suffices.

Fig. S3 : Visual ablation over the number of guide slices, for a case of mild through-plane misregistration at $8\times$ acceleration; the companion to Figure S2 , which gives a severe case. Here slice $+0$ is already the best match at $36.30$ % NRMSE against the target, the three-slice window captures what is available, and $N_{g}=5$ adds nothing on NRMSE or SSIM ( $7.54$ % / $82.36$ % against $7.40$ % / $82.81$ %), improving only LPIPS.

Fig. S4 : Visual comparison with an accelerated guide, supporting Section IV-E . (A) Unguided reconstruction, LGGS given the accelerated guide, LGGS given the fully sampled guide, and the target. (B) The guide as supplied to the network alongside the fully sampled prior it approximates, which bounds how much of the degradation is attributable to the guide itself. NRMSE / SSIM / LPIPS ( $\times 100$ ), with respect to the fully sampled target, are given above each panel.

Fig. S5 : What a magnitude guide discards, for the first case of Figure S1 . The local variation of the fully sampled examination splits into $\lVert\nabla\bm{r}\rVert$ , which a magnitude guide retains, and $\lVert\bm{r}\odot\nabla\bm{\varphi}\rVert$ , which it discards; both are pooled over the $7\times 7$ analysis support, the scale at which the codes are formed, and share one color key, so their magnitudes may be read against each other. The discarded channel holds structure the retained one does not, and repeats between visits. Hue gives phase in the first column.

Fig. S6 : As Figure S5 , for the second case of Figure S1 .

Fig. S7 : SSIM against effective acceleration, averaged over the brain-support mask (left) and over the whole frame (right), on a shared vertical scale. Otherwise as the SSIM panel of Figure 3 .

Name	$K$	$p$	$M$	$M_{h}$	$W_{z}$	$W_{g}$	$N_{g}$	params
LPDSNet	30	7	169	–	–	–	0	1.00 M
LGGS	30	7	169	64	1	3	3	1.08 M

TABLE S1 : Unrolled sparse-coding architectures.

p

is the filter support and

W_{z}

W_{g}

the self- and guide-similarity windows. LPDSNet forms no adjacency, so its attention columns do not apply.

Name	cascades	U-Net chan.	pools	sense chan.	sense pools	CG iters	$N_{g}$	params
E2EVarNet	12	18	4	8	4	–	0	33.3 M
L-TGVN	6	18	4	8	4	10	3	43.6 M

TABLE S2 : Variational-net architectures. L-TGVN adds the trust-region projection

\mathcal{P}_{\delta}

of ( 2 ), solved by conjugate gradient (CG).

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L-TGVN: Leveraging Longitudinal Priors for Personalized Rapid MRI

Arda Atalık, Sumit Chopra, Daniel K. Sodickson

NYU Center for Data Science, NY, USA · Center for Advanced Imaging Innovation and Research (CAI²R), Department of Radiology, NYU Grossman School of Medicine, NY, USA · Courant Institute of Mathematical Sciences, NY, USA+1

Accelerated MRI Reconstruction Magnetic Resonance Imaging

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MRI provides excellent soft-tissue contrast without ionizing radiation, but long acquisition times increase patient discomfort while also raising exam costs and limiting scanner throughput. A common approach to reduce scan time is to acquire fewer measurements, which yields an ill-posed linear inverse problem; recovering diagnostic-quality images therefore requires incorporating prior knowledge beyond the measured data. In follow-up exams, the most recent prior scan of a patient can provide a highly informative subject-specific context, but practical use is complicated by temporal changes (including pathology progression), misalignment between scans, and protocol drift across acquisitions. In this work, we introduce L-TGVN, a Longitudinal Trust-Guided Variational Network that leverages prior scans as side information to reconstruct the current scan from heavily undersampled measurements. Crucially, L-TGVN constrains the influence of prior scans to be consistent with the acquired measurements. Unlike many existing longitudinal reconstruction methods, it does not require explicit pre-registration between prior and current scans. It further accommodates differences in acquisition protocols across visits (e.g., changes in sequence parameters). We evaluate L-TGVN against matched-capacity baselines, including prior-guided methods and methods that do not use longitudinal priors, and observe consistent improvements in standard quantitative metrics together with better preservation of fine structures at challenging accelerations. Source code is available at github.com/sodicksonlab/L-TGVN.

Abstract

Accelerated MRI Reconstruction

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