MRI Reconstruction Risk Estimation from Inference Dynamics

Tamir Shor; Alex Bronstein

cs.CVOct 19, 2026

MRI Reconstruction Risk Estimation from Inference Dynamics

Authors: Tamir Shor, Alex Bronstein

Organizations: Technion · Institute of Science and Technology Austria

Abstract

Iterative MRI reconstructors produce intermediate estimates before returning a final image. We study these inference trajectories as a model-internal representation of realized reconstruction risk, measured by log-NMSE. Model-native states are projected to magnitude images, summarized by a fixed 16-dimensional descriptor, and mapped to risk using a source-trained ridge readout. Across three reconstruction backbones, trajectory features are strongly predictive of reconstruction risk on held-out source data. Under zero-shot target shift, their behavior is backbone-dependent, exhibiting both preserved positive association and readout reversal. Conditional analyses show that trajectory information can remain associated with error beyond an initialization-only predictor. A prefix analysis further shows that useful trajectory information can emerge before reconstruction completes. Repeated-mask and low-shot calibration studies indicate that trajectories primarily encode persistent case difficulty, while their orientation and calibration can change under domain shift.

Figures & tables

Figure 1: Method overview - (a) Intermediate reconstructions from an iterative solver are projected to a common image-space trajectory, summarized by a 16-dimensional descriptor, and mapped to predicted reconstruction risk. (b) Low- and high-risk cases can have plausible final reconstructions but exhibit different trajectory dynamics and residual error. (c) The same trajectory descriptor is applied across reconstruction backbones.

Backbone	Steps	Projected state
XPDNet	25	primal-dual image estimate
VarNet	12	sensitivity-reduced cascade output
PromptMR+	12	central image with five-slice context

Table 1: Matched trajectory construction. Projection is model-specific, while the 16 feature functions are shared.

	XPDNet		VarNet		PromptMR+
Method	$r$	$\rho_{s}$	$r$	$\rho_{s}$	$r$	$\rho_{s}$
Trajectory	$+0.804\pm 0.027$	$+0.807\pm 0.026$	$+0.849\pm 0.024$	$+0.834\pm 0.022$	$+0.906\pm 0.016$	$+0.895\pm 0.017$
Hu-style	$+0.805\pm 0.028$	$+0.774\pm 0.030$	$+0.757\pm 0.029$	$+0.734\pm 0.033$	$+0.616\pm 0.039$	$+0.563\pm 0.045$
ResNet †	$+0.911\pm 0.014$	$+0.900\pm 0.015$	$+0.588\pm 0.050$	$+0.551\pm 0.051$	$+0.187\pm 0.052$	$+0.136\pm 0.061$
CQR	$+0.790\pm 0.031$	$+0.786\pm 0.028$	$+0.819\pm 0.022$	$+0.823\pm 0.024$	$+0.855\pm 0.018$	$+0.860\pm 0.019$
RM-RMS	$-0.023\pm 0.062$	$-0.022\pm 0.070$	$-0.246\pm 0.065$	$-0.282\pm 0.068$	$-0.115\pm 0.054$	$-0.182\pm 0.065$

Table 2: Matched fastMRI-brain source holdout. Values are signed correlations with log-NMSE and are reported as estimate

\pm

patient-cluster bootstrap SD from 10,000 replicates for all three backbones. CQR uses normalized mean interval width. RM-RMS uses normalized RMS interval width. † The table reports the pre-specified source-selected ResNet realization. Additional training seeds show substantial target variability in Supplementary Table S15.

Backbone	Trajectory	Hu-style	ResNet †
XPDNet	$0.231\pm 0.014$	$0.228\pm 0.011$	$0.188\pm 0.007$
VarNet	$0.193\pm 0.011$	$0.240\pm 0.010$	$0.324\pm 0.014$
PromptMR+	$0.169\pm 0.010$	$0.316\pm 0.017$	$0.492\pm 0.022$

Table 3: Source log-NMSE RMSE for matched point predictors. Values are estimate

\pm

patient-cluster bootstrap SD from 10,000 replicates. Lower is better.

	XPDNet		VarNet		PromptMR+
Method	$r$	$\rho_{s}$	$r$	$\rho_{s}$	$r$	$\rho_{s}$
Trajectory	$+0.630\pm 0.086$	$+0.662\pm 0.090$	$-0.935\pm 0.020$	$-0.924\pm 0.030$	$+0.856\pm 0.043$	$+0.852\pm 0.052$
Hu-style	$+0.651\pm 0.099$	$+0.647\pm 0.113$	$-0.746\pm 0.072$	$-0.731\pm 0.092$	$+0.648\pm 0.116$	$+0.702\pm 0.109$
ResNet †	$+0.344\pm 0.113$	$+0.389\pm 0.129$	$+0.308\pm 0.152$	$+0.329\pm 0.161$	$+0.292\pm 0.207$	$+0.313\pm 0.191$
CQR	$+0.298\pm 0.222$	$+0.196\pm 0.187$	$+0.680\pm 0.067$	$+0.718\pm 0.066$	$+0.422\pm 0.184$	$+0.298\pm 0.184$
RM-RMS	$+0.289\pm 0.126$	$+0.270\pm 0.161$	$-0.917\pm 0.020$	$-0.922\pm 0.025$	$+0.096\pm 0.139$	$+0.092\pm 0.174$

Table 4: Matched M4Raw scan-level zero-shot transfer. Values are signed correlations with log-NMSE. Negative values indicate a reversed source-trained readout. Uncertainty follows Table 2 .

Backbone	Trajectory	Hu-style	ResNet †
XPDNet	$0.225\pm 0.020$	$0.417\pm 0.017$	$0.192\pm 0.025$
VarNet	$6.538\pm 0.215$	$4.403\pm 0.054$	$4.317\pm 0.033$
PromptMR+	$0.459\pm 0.018$	$0.165\pm 0.023$	$0.989\pm 0.025$

Table 5: M4Raw zero-shot log-NMSE RMSE for matched point predictors. Values are estimate

\pm

patient-cluster bootstrap SD.

Figure 2: PromptMR+ M4Raw cases prioritized by trajectory risk when individual baselines under-rank the error. Hu denotes the Hu-style comparator.

Score	Pooled	Between	Within	Partial
Amplitude	$0.9505$ $\pm 0.0128$	$0.9507$ $\pm 0.0139$	$0.6704$ $\pm 0.0347$	$0.4066$ $\pm 0.0491$
Trajectory	$0.9660$ $\pm 0.0062$	$0.9763$ $\pm 0.0056$	$-0.1205$ $\pm 0.0405$	$0.1419$ $\pm 0.0412$
Mask density	–	–	$0.6929$ $\pm 0.0168$	–

Table 6: Repeated-mask Spearman associations for the discovery model on the frozen 100-volume test subset of 800 volume-mask reconstructions. Values are estimate

\pm

source-volume-cluster bootstrap SD from 5,000 replicates. Between averages the eight masks within each volume. Within centers predictions and targets within physical volume. Partial correlation additionally removes realized mask density. The mask-density control uses the canonical cluster-LOO mask-fraction predictor.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Stored name	Definition	Role
trajectory_path_length	$\sum_{t=1}^{T}d_{t}$	Total normalized solver motion
trajectory_endpoint_displacement	$\operatorname{RMS}(q_{T}-q_{0})/s_{0}$	Net motion from initialization to output
trajectory_path_efficiency	endpoint displacement divided by path length	Directness of the image path
trajectory_step_mean	mean of $\{d_{t}\}$	Typical update magnitude
trajectory_step_std	population SD of $\{d_{t}\}$	Variation in update magnitude
trajectory_step_max	maximum of $\{d_{t}\}$	Largest update

Appendix

Table 7: Shared 16-dimensional descriptor used without definition changes for XPDNet, VarNet, and PromptMR+. Stored names are retained from the frozen helper.

Split	Method	$r\pm\mathrm{SD}$	95% CI	$\rho_{s}\pm\mathrm{SD}$	95% CI
Source	Trajectory	$+0.849\pm 0.024$	$[0.796,0.891]$	$+0.834\pm 0.022$	$[0.784,0.871]$
	Hu-style	$+0.757\pm 0.029$	$[0.694,0.808]$	$+0.734\pm 0.033$	$[0.661,0.791]$
	ResNet	$+0.588\pm 0.050$	$[0.481,0.675]$	$+0.551\pm 0.051$	$[0.442,0.639]$
	CQR	$+0.819\pm 0.022$	$[0.773,0.858]$	$+0.823\pm 0.024$	$[0.769,0.863]$
	RM-RMS	$-0.246\pm 0.065$	$[-0.374,-0.120]$	$-0.282\pm 0.068$	$[-0.414,-0.146]$
	Trajectory+Hu-style	$+0.895\pm 0.017$	$[0.858,0.924]$	$+0.883\pm 0.018$	$[0.843,0.912]$

Appendix

Table 8: VarNet matched results with patient-cluster uncertainty. Every metric is estimate

\pm

bootstrap SD followed by its 95% percentile CI. Target values are signed zero-shot correlations.

Split	Method	$r\pm\mathrm{SD}$	95% CI	$\rho_{s}\pm\mathrm{SD}$	95% CI
Source	Trajectory	$+0.906\pm 0.016$	$[0.870,0.935]$	$+0.895\pm 0.017$	$[0.854,0.923]$
	Hu-style	$+0.616\pm 0.039$	$[0.531,0.686]$	$+0.563\pm 0.045$	$[0.467,0.644]$
	ResNet	$+0.187\pm 0.052$	$[0.083,0.284]$	$+0.136\pm 0.061$	$[0.014,0.252]$
	CQR	$+0.855\pm 0.018$	$[0.817,0.887]$	$+0.860\pm 0.019$	$[0.816,0.892]$
	RM-RMS	$-0.115\pm 0.054$	$[-0.220,-0.006]$	$-0.182\pm 0.065$	$[-0.305,-0.052]$
	Trajectory+Hu-style	$+0.915\pm 0.014$	$[0.884,0.940]$	$+0.904\pm 0.015$	$[0.869,0.928]$

Appendix

Table 9: PromptMR+ matched results with patient-cluster uncertainty. Formatting follows Table 8 .

Split	Method	$r\pm\mathrm{SD}$	95% CI	$\rho_{s}\pm\mathrm{SD}$	95% CI
Source	Trajectory	$+0.804\pm 0.027$	$[0.748,0.852]$	$+0.807\pm 0.026$	$[0.749,0.850]$
	Hu-style	$+0.805\pm 0.028$	$[0.742,0.854]$	$+0.774\pm 0.030$	$[0.707,0.827]$
	ResNet	$+0.911\pm 0.014$	$[0.880,0.936]$	$+0.900\pm 0.015$	$[0.867,0.924]$
	CQR	$+0.790\pm 0.031$	$[0.725,0.844]$	$+0.786\pm 0.028$	$[0.724,0.833]$
	RM-RMS	$-0.023\pm 0.062$	$[-0.145,0.097]$	$-0.022\pm 0.070$	$[-0.159,0.115]$
M4Raw	Trajectory	$+0.630\pm 0.086$	$[0.440,0.775]$	$+0.662\pm 0.090$	$[0.447,0.800]$

Appendix

Table 10: XPDNet matched results with patient-cluster uncertainty. Every metric is estimate

\pm

bootstrap SD followed by its 95% percentile CI. Target values are signed zero-shot correlations. CQR uses normalized mean interval width.

Backbone	Split	Method	RMSE $\pm$ SD	95% CI
XPDNet	Source	Trajectory	$0.231\pm 0.014$	$[0.204,0.258]$
		Hu-style	$0.228\pm 0.011$	$[0.208,0.250]$
		ResNet	$0.188\pm 0.007$	$[0.174,0.202]$
	M4Raw	Trajectory	$0.225\pm 0.020$	$[0.184,0.262]$
		Hu-style	$0.417\pm 0.017$	$[0.383,0.450]$
		ResNet	$0.192\pm 0.025$	$[0.144,0.240]$

Appendix

Table 11: RMSE of matched point predictors. Each completed value is estimate

\pm

patient-cluster bootstrap SD with 95% CI. Lower is better. Large VarNet target RMSEs reflect failed source calibration and orientation under zero-shot transfer.

Backbone	Difference	$\Delta r\pm\mathrm{SD}$	95% CI	$\Delta\rho_{s}\pm\mathrm{SD}$	95% CI
VarNet	Trajectory $-$ Hu-style	$-0.189\pm 0.072$	$[-0.351,-0.068]$	$-0.193\pm 0.093$	$[-0.408,-0.049]$
	Trajectory $-$ ResNet	$-1.243\pm 0.152$	$[-1.515,-0.926]$	$-1.253\pm 0.163$	$[-1.520,-0.891]$
	Trajectory $-$ CQR	$-1.615\pm 0.075$	$[-1.739,-1.448]$	$-1.643\pm 0.075$	$[-1.737,-1.442]$
	Trajectory $-$ RM-RMS	$-0.018\pm 0.022$	$[-0.062,0.025]$	$-0.002\pm 0.029$	$[-0.058,0.057]$
PromptMR+	Trajectory $-$ Hu-style	$+0.209\pm 0.118$	$[0.002,0.457]$	$+0.149\pm 0.111$	$[-0.014,0.409]$
	Trajectory $-$ ResNet	$+0.564\pm 0.220$	$[0.147,1.019]$	$+0.539\pm 0.204$	$[0.164,0.958]$

Appendix

Table 12: Paired M4Raw comparisons. A row labeled trajectory minus comparator uses that direction. VarNet and PromptMR+ report estimate

\pm

bootstrap SD and 95% CI. XPDNet reports the point difference and 95% CI. The XPDNet fusion row uses fusion minus trajectory.

Backbone	Prediction corr.	Partial measure	Trajectory given Hu-style	Hu-style given trajectory
PromptMR+	$r=0.712$	Pearson	$0.739\pm 0.111$ $[0.430,0.868]$	$0.104\pm 0.205$ $[-0.291,0.499]$
	$\rho_{s}=0.725$	Spearman	$0.698\pm 0.122$ $[0.393,0.858]$	$0.235\pm 0.173$ $[-0.134,0.526]$
VarNet	$r=0.713$	Pearson	$-0.863\pm 0.052$ $[-0.935,-0.731]$	$-0.320\pm 0.113$ $[-0.536,-0.087]$
	$\rho_{s}=0.677$	Spearman	$-0.855\pm 0.067$ $[-0.926,-0.666]$	$-0.375\pm 0.122$ $[-0.588,-0.101]$
XPDNet	$r=0.421$	Pearson	$0.517$ $[0.341,0.679]$	$0.548$ $[0.316,0.729]$
	$\rho_{s}=0.441$	Spearman	$0.550$ $[0.343,0.708]$	$0.529$ $[0.213,0.709]$

Appendix

Table 13: Conditional association with M4Raw log-NMSE after controlling for the other score. VarNet and PromptMR+ report estimate

\pm

bootstrap SD and 95% CI. XPDNet reports estimate and 95% CI.

Backbone	Split	Measure	Trajectory given $q_{0}$	$q_{0}$ given trajectory
PromptMR+	Source	Pearson	$0.9011\pm 0.0167$ $[0.8654,0.9299]$	$-0.0004\pm 0.0736$ $[-0.1460,0.1415]$
		Spearman	$0.8894\pm 0.0178$ $[0.8492,0.9184]$	$0.0404\pm 0.0811$ $[-0.1195,0.1959]$
	M4Raw	Pearson	$0.6440\pm 0.0749$ $[0.4696,0.7613]$	$0.5807\pm 0.1228$ $[0.2971,0.7694]$
		Spearman	$0.6663\pm 0.0828$ $[0.4658,0.7913]$	$0.5266\pm 0.1548$ $[0.1436,0.7485]$
VarNet	Source	Pearson	$0.7721\pm 0.0327$ $[0.6983,0.8267]$	$0.3867\pm 0.0542$ $[0.2754,0.4887]$
		Spearman	$0.7498\pm 0.0340$ $[0.6745,0.8070]$	$0.3203\pm 0.0574$ $[0.2036,0.4305]$

Appendix

Table 14: Conditional association with log-NMSE for trajectory and initialization. Values are estimate

\pm

patient-cluster bootstrap SD with 95% percentile CI from 10,000 replicates. Each column residualizes the named score against the other score.

Backbone	Split	Full		$s_{0}$ -independent
		$r$	$\rho_{s}$	$r$	$\rho_{s}$
VarNet	Source	$0.8488$	$0.8342$	$0.8183$	$0.7961$
	M4Raw	$-0.9347$	$-0.9242$	$-0.9575$	$-0.9482$
PromptMR+	Source	$0.9061$	$0.8947$	$0.8840$	$0.8825$
	M4Raw	$0.8565$	$0.8517$	$0.8443$	$0.8572$

Appendix

Table 15: Initialization-normalization diagnostic. Full uses all 16 components. The

s_{0}

-independent model uses the ten components whose values do not depend on the

q_{0}

-based scale normalizer after algebraic cancellation. Ridge regularization is reselected using source-only five-fold patient-level cross-validation. Values are descriptive source-trained point estimates.

Prefix	Source $r$	Source $\rho_{s}$	Source RMSE	Target $r$	Target $\rho_{s}$
12/25	$0.7005$	$0.6961$	$0.2740$	$0.6224$	$0.6228$
25/25	$0.8036$	$0.8068$	$0.2311$	$0.6303$	$0.6618$

Appendix

Table 16: XPDNet source-only trajectory prediction using 12 of 25 or all 25 iterations. Target values use the matched M4Raw cohort. RMSE is reported where evaluated.

Backbone	Pearson $r$	Spearman $\rho_{s}$
XPDNet	$0.5800$	$0.5343$
VarNet	$-0.9236$	$-0.8508$
PromptMR+	$0.5234$	$0.5004$

Appendix

Table 17: M4Raw association after centering score and log-NMSE within patient. Values are descriptive scan-level point estimates.

Backbone	Score	Source $r$	Source $\rho_{s}$	M4Raw $r$	M4Raw $\rho_{s}$
VarNet	Final DC residual	$0.2142$	$0.1086$	$0.9741$	$0.9658$
	Endpoint amplitude	$-0.0097$	$-0.0117$	$0.1504$	$0.1900$
	Trajectory+controls	$0.8708$	$0.8570$	$-0.9185$	$-0.8956$
PromptMR+	Final DC residual	$-0.1417$	$-0.1628$	$0.1488$	$0.2064$
	Endpoint amplitude	$-0.0086$	$-0.0231$	$0.0835$	$0.0602$
	Trajectory+controls	$0.9097$	$0.8974$	$0.8459$	$0.8459$

Appendix

Table 18: Backbone-specific endpoint and physics-side diagnostics used to interpret the distinct VarNet and PromptMR+ transfer results. Trajectory+controls is a 19-input source-trained joint readout comprising the 16 trajectory features, endpoint amplitude, the final data-consistency residual, and mask density. Values are descriptive point estimates, while primary inference uses the matched tables.

Split	Mean	Median	5th pct.	95th pct.
Source	$0.00666$	$0.00609$	$0.00358$	$0.01142$
M4Raw	$2.438$	$2.418$	$1.650$	$3.401$

Appendix

Table 19: VarNet slice-level reconstruction NMSE under the matched source and target protocol. These values describe reconstruction error rather than risk-prediction RMSE.

Patients	Traj. RMSE	Constant RMSE	Difference	Test $r$
4	$0.0924\pm 0.0172$	$0.2306\pm 0.0270$	$-0.1383\pm 0.0282$	$0.9348\pm 0.0093$
8	$0.0837\pm 0.0100$	$0.2205\pm 0.0199$	$-0.1368\pm 0.0206$	$0.9348\pm 0.0148$
16	$0.0795\pm 0.0130$	$0.2144\pm 0.0272$	$-0.1349\pm 0.0285$	$0.9327\pm 0.0303$

Appendix

Table 20: Matched VarNet low-shot affine repair. Values are mean

\pm

SD across repeated patient-held-out splits. Difference is trajectory minus target-constant RMSE.

Seed	Source $r$	Source $\rho_{s}$	Source RMSE	Target $r$	Target $\rho_{s}$	Target RMSE
Reported run	$0.187$	$0.136$	$0.492$	$0.292$	$0.313$	$0.989$
20260816	$0.261$	$0.180$	$0.457$	$0.319$	$0.369$	$1.336$
20260817	$0.477$	$0.375$	$1.076$	$0.674$	$0.715$	$1.384$

Appendix

Table 21: PromptMR+ scalar ResNet seed sensitivity. For each training seed, checkpoint selection uses source data only. Values are descriptive point estimates from the source holdout and zero-shot M4Raw evaluation.

Predictor	$r$	$\rho_{s}$	RMSE	MAE
Amplitude	$0.8930$	$0.9521$	$0.3873$	$0.3278$
Trajectory	$0.9635$	$0.9718$	$0.2519$	$0.1924$
Combined	$0.9777$	$0.9787$	$0.1760$	$0.1390$
Difference	$\Delta\rho_{s}$ and 95% CI		$\Delta$ RMSE and CI	$\Delta$ MAE and CI
Trajectory $-$ amplitude	$+0.0202$ $[-0.0049,0.0528]$		$-0.1359$ $[-0.1987,-0.0794]$	$-0.1360$ $[-0.1868,-0.0870]$
Combined $-$ trajectory	$+0.0074$ $[-0.0031,0.0185]$		$-0.0758$ $[-0.1174,-0.0356]$	$-0.0538$ $[-0.0886,-0.0198]$

Appendix

Table 22: Discovery-model source prediction and paired differences. Difference rows use the first method minus the second and include 95% patient-bootstrap CIs. Inferential comparisons in the text use these paired intervals.

Score	Pooled $\rho_{s}$	Between $\rho_{s}$	Within $\rho_{s}$	Partial $\rho_{s}$
Amplitude	$0.9505\pm 0.0128$ $[0.9172,0.9662]$	$0.9507\pm 0.0139$ $[0.9147,0.9681]$	$0.6704\pm 0.0347$ $[0.5980,0.7354]$	$0.4066\pm 0.0491$ $[0.3127,0.5046]$
Trajectory	$0.9660\pm 0.0062$ $[0.9480,0.9720]$	$0.9763\pm 0.0056$ $[0.9604,0.9825]$	$-0.1205\pm 0.0405$ $[-0.2004,-0.0419]$	$0.1419\pm 0.0412$ $[0.0593,0.2215]$
Mask density	–	–	$0.6929\pm 0.0168$ $[0.6587,0.7247]$	–

Appendix

Table 23: Discovery-model repeated-mask Spearman associations on the frozen 100-volume test subset. Values are estimate

\pm

source-volume-cluster bootstrap SD with 95% percentile CI from 5,000 replicates. Between averages masks within volume. Within centers predictions and targets within volume. Partial correlation additionally removes realized mask density. Mask density uses the cluster-LOO mask-fraction predictor.

Cohort	Model	Slope	95% CI
Adaptation	Pooled	$-0.916$	$[-1.254,-0.577]$
	Patient+acquisition	$-0.546$	$[-0.700,-0.399]$
	Strict	$-0.434$	$[-0.615,-0.246]$
Confirmation	Pooled	$-1.383$	$[-1.641,-1.127]$
	Patient+acquisition	$-0.323$	$[-0.572,-0.122]$
	Strict	$-0.187$	$[-0.438,0.0002]$

Appendix

Table 24: PromptMR severe-shift slopes with 95% patient-bootstrap CIs. Strict models add endpoint amplitude and mask density to patient and acquisition effects.

Patients	Constant	Amplitude	Trajectory	Traj. $-$ constant	Traj. $-$ amplitude	Reduction
4	$0.6921$	$0.6810$	$0.6464$	$-0.0457$ $[-0.0618,-0.0301]$	$-0.0346$ $[-0.0556,-0.0140]$	$6.6\%$
8	$0.6888$	$0.6777$	$0.6384$	$-0.0504$ $[-0.0702,-0.0312]$	$-0.0393$ $[-0.0774,-0.0014]$	$7.3\%$
16	$0.6883$	$0.6778$	$0.6452$	$-0.0431$ $[-0.0577,-0.0290]$	$-0.0325$ $[-0.0682,0.0034]$	$6.3\%$

Appendix

Table 25: Low-shot affine calibration on the severe PromptMR shift. Paired differences are trajectory minus comparator RMSE with 95% patient-bootstrap CI.

Measurement	Value
Replicated relation-direction cosine	$0.5156\pm 0.0893$
Cosine with negative loss gradient	$0.000503\pm 0.000583$
Single-case true-gradient PSNR change	$+0.00855$ dB
Single-case reverse predicted-direction PSNR change	$+0.000047$ dB

Appendix

Table 26: Controlled-corruption pilot. The first two rows summarize the eight-image, three-realization directional replication. The final two rows are from the separate single-case leverage probe at

\beta=0.1

Image Reconstruction

Image reconstruction recovers images, volumes, or scenes from incomplete, noisy, indirect, or compressed measurements using physical models and learned priors.

See all 288 papers

Trajectory Constraints for Imaging Inverse Problems
May 27, 2026Chaoyan Huang, Haijie Yuan, Bharath Subramanian +1Proximal Optimization Image Reconstruction
Department of Computational Mathematics, Science, & Engineering, Michigan State University · Department of Electrical Engineering and Computer Science, University of Michigan · Department of Biomedical Engineering, Michigan State University
Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors
Aug 18, 2026Mahdi Saberi, Yaşar Utku Alçalar, Merve Gülle +2Accelerated MRI Reconstruction Magnetic Resonance Imaging
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA · Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, USA · Department of Medicine (Cardiology), University of Minnesota, Minneapolis, MN, USA
Next-Acceleration-Scale Prediction for Autoregressive MRI Reconstruction
May 19, 2026Yilmaz Korkmaz, Vishal M. PatelVisual Autoregressive Models Computational Imaging
Johns Hopkins University, Baltimore MD 21218, USA

May 27, 2026J/K move · Enter open · S save

Trajectory Constraints for Imaging Inverse Problems

Chaoyan Huang, Haijie Yuan, Bharath Subramanian, Saiprasad Ravishankar

Department of Computational Mathematics, Science, & Engineering, Michigan State University · Department of Electrical Engineering and Computer Science, University of Michigan · Department of Biomedical Engineering, Michigan State University

Proximal Optimization Image Reconstruction Computational Imaging Diffusion-Based Inverse Problems Inverse Problems Image Inverse Problems

Open paper AskPDF arXiv

Diffusion models have achieved strong performance in imaging inverse problems, but typically rely on domain-matched pretrained models and external training data. Moreover, errors introduced at intermediate reverse-sampling steps can accumulate and degrade the final reconstruction, with their propagation strongly influenced by how successive states are related. We propose TRACE, a training-free TRAjectory-Constrained rEconstruction framework for imaging inverse problems. TRACE replaces the pretrained diffusion model with an untrained overparameterized network optimized directly from the observed measurements and organizes reconstruction as a sequence of intermediate states. At each step, TRACE enforces stochastic proximal consistency (SPC) by inferring each reconstruction from a stochastically perturbed predecessor under measurement consistency, while proximally constraining the resulting estimate to its corresponding unperturbed state. This formulation admits a proximal interpretation, from which we derive stability bounds characterizing the variation between consecutive states under approximate network updates. A local Jacobian analysis further characterizes how SPC regularizes the network-parameterized reconstruction. Experiments on natural-image restoration and CT reconstruction demonstrate competitive performance against both untrained and pretrained neural-prior methods. We further show that the proposed trajectory constraint can be incorporated into existing diffusion-based inverse solvers to improve reconstruction performance.

Abstract

Image Reconstruction

Explore similar work

Trajectory Constraints for Imaging Inverse Problems

Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors

Next-Acceleration-Scale Prediction for Autoregressive MRI Reconstruction