EMORe: Adaptive 5D Cardiac MRI Reconstruction

• EMORe is an adaptive 5D cardiac MRI reconstruction method that uses expectation–maximization to reassign readouts across cardiac–respiratory bins and reject outliers.
• It employs a soft binning approach with weighted compressed-sensing and TV regularization to enhance image sharpness and reduce motion artifacts.
• Validation in phantom and in vivo studies demonstrated improved binning accuracy, edge sharpness, and artifact reduction compared to standard self-gated methods.

Searching arXiv for "EMORe" to ground the article in current papers. EMORe most directly denotes “Expectation–Maximization-guided binning correction and outlier rejection,” a model-based reconstruction framework for free-running, free-breathing self-gated 5D cardiac magnetic resonance imaging (MRI) that replaces hard self-gating bin assignments with adaptive, probabilistic participation across cardiac–respiratory bins and an explicit outlier bin, updated within an EM loop and coupled to a weighted compressed-sensing reconstruction with spatial and motion-dimension total-variation regularization (Arshad et al., 31 Jul 2025). The method was introduced to address two failure modes of conventional self-gated 5D MRI reconstruction: valid data placed in the wrong motion bin and motion-corrupted outliers that contaminate nominal bins, both of which degrade image sharpness and increase motion artifacts (Arshad et al., 31 Jul 2025). In a separate and unrelated usage, “EMORe” is also described as an informal shorthand or alias for EMO-R3, a reinforcement-learning framework for emotional reasoning in multimodal LLMs; that aliasing does not refer to the MRI method (Fang et al., 27 Feb 2026).

1. Definition and scope

EMORe is an adaptive reconstruction method designed for free-running, free-breathing self-gated 5D cardiac MRI, where a 3D volume is resolved over two temporal motion dimensions—cardiac phase and respiratory phase—yielding $x(r,c)$ with $K=N_{\text{resp}}\times N_{\text{card}}$ bins, exemplified as $4\times 20=80$ (Arshad et al., 31 Jul 2025). In this setting, conventional retrospective motion binning assigns each readout to one motion bin via hard classification. EMORe departs from that formulation by treating the true bin labels as latent variables and by allowing readouts either to distribute probabilistically across valid bins or to be rejected into a dedicated outlier bin (Arshad et al., 31 Jul 2025).

The method was motivated by limitations of standard self-gating pipelines. Self-gating signals are extracted from repeatedly sampled central k-space lines via blind source separation, but inaccuracies in cardiac and respiratory signal extraction, irregular breathing, beat-to-beat variability, arrhythmias, and sporadic bulk motion can induce residual motion artifacts (Arshad et al., 31 Jul 2025). The paper identifies two dominant failure modes: inter-bin leakage from misassignment of valid data, and contamination from motion-corrupted outliers that do not belong to any nominal cardiorespiratory state (Arshad et al., 31 Jul 2025).

This framing suggests that EMORe is best understood not merely as a reconstruction algorithm, but as a latent-state correction layer inserted between self-gating-based motion estimation and compressed-sensing image recovery. A plausible implication is that its main contribution is to make existing free-running 5D MRI pipelines more tolerant of imperfect physiological binning without requiring explicit motion fields (Arshad et al., 31 Jul 2025).

2. Acquisition model, variables, and reconstruction objective

The acquisition model assumes free-running, free-breathing self-gated imaging with a 3D pseudo-random Cartesian trajectory and periodic center-of-k-space readouts every 10 readouts for self-gating (Arshad et al., 31 Jul 2025). Surrogate respiratory signals are extracted in the $0.1$–$0.5$ Hz band and cardiac signals in the $0.5$–$3$ Hz band by filtering the self-gating readouts arranged in a Casorati matrix, followed by PCA/ICA (Arshad et al., 31 Jul 2025). Retrospective hard binning partitions the respiratory signal into four equipopulated respiratory bins and the R–R interval into 20 equal-duration cardiac bins, producing $K=80$ bins and an initial hard assignment $g_n\in\{1,\dots,K\}$ for readout $n$ (Arshad et al., 31 Jul 2025).

The forward model represents the acquired data as $K=N_{\text{resp}}\times N_{\text{card}}$0, with $K=N_{\text{resp}}\times N_{\text{card}}$1 multi-coil readouts $K=N_{\text{resp}}\times N_{\text{card}}$2, and the image sequence as $K=N_{\text{resp}}\times N_{\text{card}}$3 with $K=N_{\text{resp}}\times N_{\text{card}}$4 encoding the complex-valued 3D image at motion state $K=N_{\text{resp}}\times N_{\text{card}}$5 (Arshad et al., 31 Jul 2025). Coil sensitivity maps are estimated with Walsh and embedded in the bin/readout-specific forward operators $K=N_{\text{resp}}\times N_{\text{card}}$6, which perform multiplication by sensitivity maps, 3D Fourier transform, and selection of the $K=N_{\text{resp}}\times N_{\text{card}}$7th readout sampling pattern for bin $K=N_{\text{resp}}\times N_{\text{card}}$8 (Arshad et al., 31 Jul 2025). Under a circular complex Gaussian noise model,

$K=N_{\text{resp}}\times N_{\text{card}}$9

where $4\times 20=80$0 is the unknown latent bin label and $4\times 20=80$1 is the per-complex-dimension noise variance (Arshad et al., 31 Jul 2025).

Given soft participation weights $4\times 20=80$2, the M-step minimizes a weighted least-squares objective with 5D total-variation regularization:

$4\times 20=80$3

with

$4\times 20=80$4

Here, $4\times 20=80$5 applies anisotropic TV across spatial axes within each bin, $4\times 20=80$6 applies TV along the cardiac dimension across bins with the same respiratory phase, and $4\times 20=80$7 applies TV along the respiratory dimension across bins with the same cardiac phase (Arshad et al., 31 Jul 2025).

This design places EMORe squarely within regularized inverse-problem reconstruction, but with the data fidelity term modulated by posterior bin participation rather than fixed bin membership. That distinction is central to its motion robustness.

3. Expectation–maximization mechanism

EMORe alternates an E-step that refines soft bin participation and an M-step that updates the image estimate, executing these steps alternately until convergence (Arshad et al., 31 Jul 2025). The latent label space is extended from $4\times 20=80$8 to $4\times 20=80$9, where $0.1$0 is a dedicated outlier bin (Arshad et al., 31 Jul 2025).

In the E-step, the posterior participation of readout $0.1$1 in bin $0.1$2 at iteration $0.1$3 is

$0.1$4

For valid bins $0.1$5, the likelihood is

$0.1$6

whereas for the outlier bin,

$0.1$7

with $0.1$8 a user-chosen outlier scale (Arshad et al., 31 Jul 2025). Smaller $0.1$9 pushes more probability mass into the outlier bin, while larger $0.5$0 is more permissive (Arshad et al., 31 Jul 2025).

The prior $0.5$1 is an SG-informed categorical prior:

$0.5$2

for all other valid bins, with typical values $0.5$3 and $0.5$4 (Arshad et al., 31 Jul 2025). This prior stabilizes EM in high dimensions by retaining confidence in the original self-gating label while still permitting reassignment (Arshad et al., 31 Jul 2025).

The M-step uses the refined weights for $0.5$5 and solves the weighted least-squares plus TV problem; outlier-bin weights do not contribute to the data fidelity term, so outlier data are effectively removed (Arshad et al., 31 Jul 2025). EMORe uses a generalized EM in which the M-step is solved approximately by $0.5$6 ADMM iterations with standard variable splitting for the TV terms and weighted least-squares updates for the $0.5$7-subproblem (Arshad et al., 31 Jul 2025).

The paper interprets this E-step as implementing adaptive inter-bin correction and explicit outlier rejection simultaneously. Readouts migrate away from bins whose current images predict large residuals and toward bins with better agreement, while persistently inconsistent readouts are absorbed by the outlier bin (Arshad et al., 31 Jul 2025). No hand-crafted neighborhood smoothing across motion dimensions is required; redistribution is data- and prior-driven (Arshad et al., 31 Jul 2025).

4. Initialization, implementation, and computational profile

EMORe initializes weights using the hard self-gating assignments,

$0.5$8

and computes a warm-start image $0.5$9 by running $0.5$0 ADMM iterations of the M-step with these binary weights (Arshad et al., 31 Jul 2025). The algorithm then alternates E- and M-steps for at most $0.5$1 EM iterations, or until the normalized squared difference criterion

$0.5$2

is met (Arshad et al., 31 Jul 2025). Typical settings are $0.5$3, $0.5$4, $0.5$5, and $0.5$6 (Arshad et al., 31 Jul 2025).

Unless otherwise noted, the regularization and prior hyperparameters are $0.5$7, $0.5$8, $0.5$9, $3$0, $3$1, and $3$2 (Arshad et al., 31 Jul 2025). The method was implemented in MATLAB with GPU acceleration on an NVIDIA H100 (Arshad et al., 31 Jul 2025).

The compressed-sensing comparator uses the same M-step objective and ADMM solver but keeps the initial binary weights fixed for all iterations, corresponding to a standard SG-based binning reconstruction with spatial and cardiorespiratory TV regularization (Arshad et al., 31 Jul 2025). This makes the comparison methodologically narrow and interpretable: the difference is the adaptive EM-based weighting rather than a change of regularizer or solver (Arshad et al., 31 Jul 2025).

The added computational cost arises primarily from the E-step, which evaluates per-readout residuals against all bins to compute $3$3 (Arshad et al., 31 Jul 2025). The E-step cost scales as $3$4 residual evaluations, while the M-step is similar to compressed sensing but with weights; overall, EMORe incurs a 16–24% runtime increase in the reported setups and scales approximately linearly with $3$5 and $3$6 (Arshad et al., 31 Jul 2025). Average runtime was 23.7 min versus 19.1 min for the phantom experiments, and 58.0 min versus 49.8 min for the in vivo experiments (Arshad et al., 31 Jul 2025).

5. Validation in phantom and in vivo studies

The method was validated in both a simulated 5D MRXCAT phantom and in vivo volunteer scans (Arshad et al., 31 Jul 2025). The phantom study used five digital subjects with 4 respiratory phases and 20 cardiac phases, respiratory periods of 3.25–4.75 s with 0–1 s variability, heart rates of 62–83 bpm with 0–160 ms beat-to-beat variation, 75,000 readouts over 5 min, an 8-coil array with Biot–Savart sensitivities, and complex Gaussian noise at SNR 30 dB (Arshad et al., 31 Jul 2025). Bulk-motion corruption was simulated using seven rigid outlier states in 10 episodes per scan across 10 outlier levels from 0% to 70% of data (Arshad et al., 31 Jul 2025).

The in vivo study included 13 healthy volunteers scanned on a 3T MAGNETOM Vida with a 48-channel coil using a ferumoxytol-enhanced, free-running 5-min scan and the same blind-source-separation pipeline to form $3$7 bins (Arshad et al., 31 Jul 2025). Coil compression reduced the data to 8 virtual coils via SVD, and Walsh sensitivity estimation was again used (Arshad et al., 31 Jul 2025). Three volunteers were instructed to cough during the final 30 s to provoke bulk motion (Arshad et al., 31 Jul 2025).

The evaluation metrics included PSNR, SSIM, blood–myocardium edge sharpness, bin assignment accuracy measured by a Brier score,

$3$8

and a blinded in vivo qualitative assessment of artifacts and noise using a 5-point Likert scale (Arshad et al., 31 Jul 2025).

The principal reported results are summarized below.

Setting	EMORe result	Comparator/result
In vivo edge sharpness	$3$9	CS: $K=80$0
Reader 1 artifact score	$K=80$1	CS: $K=80$2
Reader 2 artifact score	$K=80$3	CS: $K=80$4
Phantom runtime	23.7 min	CS: 19.1 min
In vivo runtime	58.0 min	CS: 49.8 min

In the phantom with no simulated outliers, EMORe and compressed sensing had indistinguishable PSNR, SSIM, and edge sharpness, but EMORe significantly improved binning accuracy, indicating effective inter-bin correction even in the absence of explicit outliers (Arshad et al., 31 Jul 2025). As outlier fraction increased from 5% to 40%, EMORe consistently and significantly outperformed compressed sensing in PSNR, SSIM, and edge sharpness, with paired $K=80$5-tests yielding $K=80$6 across subjects (Arshad et al., 31 Jul 2025). For extreme outlier burdens above 40–70%, EMORe retained an advantage, although image quality degraded for both methods (Arshad et al., 31 Jul 2025).

In vivo, EMORe improved blood–myocardium edge sharpness from $K=80$7 to $K=80$8, and blinded artifact scores improved for both readers with Bonferroni-corrected $K=80$9 (Arshad et al., 31 Jul 2025). In the coughing experiments, the E-step assigned high outlier probabilities during the instructed motion episodes while preserving clean phases, consistent with the intended rejection behavior (Arshad et al., 31 Jul 2025).

6. Interpretation, limitations, and terminological ambiguity

The method’s central claim is that it explicitly models uncertainty in self-gating-based binning and the presence of outliers, making it robust to imperfect gating and sporadic bulk motion without requiring deformation fields or discarding whole respiratory phases (Arshad et al., 31 Jul 2025). The E-step corrects misbinned valid data through Gaussian residual-based reassignment and rejects corrupted readouts through the constant-likelihood outlier model, while the M-step reconstructs all motion states jointly with weighted data fidelity and motion-dimension sparsity (Arshad et al., 31 Jul 2025).

The paper also reports ablation-like interpretations. In the 0% outlier phantom, improved Brier score without improvement in PSNR or SSIM suggests that inter-bin correction alone improves bin accuracy while image metrics remain bounded by sampling and noise in the no-outlier regime (Arshad et al., 31 Jul 2025). At nonzero outlier levels, both inter-bin correction and outlier rejection contribute: the former recovers valid data wrongly assigned by self-gating, and the latter reduces contamination from true motion-corrupted measurements (Arshad et al., 31 Jul 2025).

Several limitations are stated explicitly. The likelihood assumes i.i.d. complex Gaussian noise and that a full readout is governed by a single motion state (Arshad et al., 31 Jul 2025). The outlier model uses a constant likelihood $g_n\in\{1,\dots,K\}$0 rather than a learned heavy-tailed model, so $g_n\in\{1,\dots,K\}$1 must be tuned (Arshad et al., 31 Jul 2025). Severe or pervasive motion above 40% outliers degrades all methods; EMORe remains advantageous but is not immune (Arshad et al., 31 Jul 2025). Very poor self-gating signals or extremely large $g_n\in\{1,\dots,K\}$2 may destabilize EM, although the prior $g_n\in\{1,\dots,K\}$3 mitigates this (Arshad et al., 31 Jul 2025). EMORe does not explicitly model inter-bin k-space phase transitions or perform explicit spatial registration between bins (Arshad et al., 31 Jul 2025).

A common misconception is that “EMORe” necessarily refers to an emotional-reasoning framework. In fact, a separate paper states that “EMO-R3 and EMORe refer to the same framework” in the context of multimodal emotional reasoning (Fang et al., 27 Feb 2026). That usage is unrelated to MRI reconstruction. In exact-title usage on arXiv, however, EMORe refers to the motion-robust 5D MRI method introduced in “EMORe: Motion-Robust 5D MRI Reconstruction via Expectation-Maximization-Guided Binning Correction and Outlier Rejection” (Arshad et al., 31 Jul 2025). This suggests that the term is overloaded across fields, and disambiguation by title or domain is essential.

7. Position within related research

EMORe is positioned as an enhancement of standard self-gating-based compressed sensing rather than a wholesale replacement of free-running 5D reconstruction (Arshad et al., 31 Jul 2025). Its baseline comparator uses the same ADMM engine and the same spatial, cardiac, and respiratory TV regularization, differing only in whether bin weights remain fixed or are updated adaptively (Arshad et al., 31 Jul 2025). This isolates EMORe’s contribution to expectation-maximization-guided binning correction and outlier rejection.

Conceptually, the method reframes self-gated 5D cardiac MRI reconstruction as a mixture-model inverse problem in which each readout has a soft affiliation to cardiorespiratory bins and an outlier bin (Arshad et al., 31 Jul 2025). That formulation is clinically motivated: the paper argues that EMORe enhances the clinical applicability and diagnostic confidence of 5D cardiac MRI by improving motion robustness under irregular breathing, intermittent bulk motion, and noisy gating signals, with only a modest runtime increase (Arshad et al., 31 Jul 2025).

Practical guidance in the paper recommends default settings of $g_n\in\{1,\dots,K\}$4, $g_n\in\{1,\dots,K\}$5, $g_n\in\{1,\dots,K\}$6, $g_n\in\{1,\dots,K\}$7, $g_n\in\{1,\dots,K\}$8, $g_n\in\{1,\dots,K\}$9, $n$0, $n$1, $n$2, and $n$3 (Arshad et al., 31 Jul 2025). For unstable EM, increasing $n$4 or reducing $n$5 is suggested; for heavy bulk motion, decreasing $n$6 or increasing $n$7 rejects more outliers at the cost of sampling efficiency (Arshad et al., 31 Jul 2025). In that sense, EMORe functions as a tunable robustness layer for free-running cardiac MRI, with its principal trade-off lying between motion tolerance and effective data retention (Arshad et al., 31 Jul 2025).