Generative Multitasking in Cardiac MRI

• Generative Multitasking is a unified image reconstruction framework that models cardiac motion as a trajectory in the complex plane using a CVAE.
• It conditions on sequence timing to disentangle motion effects from contrast and gradient artifacts, effectively suppressing trajectory-dependent artifacts.
• The framework supports both real-time playback and gated cine reconstruction from a single free-breathing, non-ECG scan, significantly enhancing quantitative mapping.

Generative Multitasking refers to a unified image reconstruction framework that enables both gated and real-time cardiac MRI (CMR), including quantitative imaging, from a single free-breathing, non-ECG-gated acquisition. The key innovation is representing cardiac motion as a trajectory in the complex plane—lifting it beyond one-dimensional phase-only models—and employing a conditional variational autoencoder (CVAE) to learn an implicit neural temporal basis. This architecture provides an interpretable latent space for cardiac and respiratory motion, supports flexible reconstruction tasks, suppresses trajectory-dependent artifacts, and improves signal-to-noise ratio (SNR) in quantitative mapping (Fang et al., 22 Nov 2025).

1. Complex-Harmonic Cardiac Coordinate System

Cardiac motion is mathematically modeled as a complex harmonic. The band-passed cardiac latent trajectory $u_{\mathrm{card}'}(t) \in \mathbb{R}$, extracted by a learned encoder and fixed band‑pass filter, is combined with its quadrature component (obtained via the discrete‑time Hilbert transform $\mathcal{H}[\cdot]$) to form the complex cardiac coordinate:

$$\widetilde{z}_{\mathrm{card}}(t) = u_{\mathrm{card}'}(t) + i \mathcal{H}[u_{\mathrm{card}'}(t)] \in \mathbb{C}.$$

The instantaneous phase $\phi(t) = \arg(\widetilde{z}_{\mathrm{card}}(t))$ characterizes cardiac phase, while the amplitude $A(t) = |\widetilde{z}_{\mathrm{card}}(t)|$ encodes beat‑to‑beat functional variability. For approximately constant heart rate,

$$\widetilde{z}_{\mathrm{card}}(t) \approx A(t) \exp(i \omega [t-\Delta t]),$$

where $\omega$ is angular frequency and $\Delta t$ is the timing offset. This coordinate system orthogonalizes cardiac phase and amplitude, enabling direct and flexible manipulation of both motion and variability (Fang et al., 22 Nov 2025).

2. Conditioning on Sequence Timing

To separate pure motion from contrast and gradient system–driven effects (notably eddy currents), both encoder and decoder are conditioned on sequence timing parameters. The conditional vector at each readout index $t$ is

$$c(t) = [t_{\mathrm{prep}(t)}, \mathrm{TI}(t), \alpha(t), k[t-\mathrm{TR}]]^T,$$

where the last term represents the previous $k$-space angle. This enables the network to learn and remove trajectory-dependent artifacts during inference. Phase encoding of the complex harmonic suffices for cardiac time mapping; contrast dependence is managed via $c(t)$. This explicit conditioning framework is crucial for robust quantitative reconstruction under free-running acquisition and heterogeneous gradients (Fang et al., 22 Nov 2025).

3. Latent Amplitude Probabilistic Modeling in CVAE

Within the CVAE, each time point yields encoder outputs $\mu_{\mathrm{card}}(t)$ and $\log \sigma_{\mathrm{card}}^2(t)$. A real-valued latent $$z_{\mathrm{card}}(t) \sim \mathcal{N}(\mu_{\mathrm{card}}(t), \sigma_{\mathrm{card}}^2(t))$$ is processed with band-pass filtering and Hilbert transform to form a complex Gaussian latent

$$\widetilde{Z}_{\mathrm{card}}(t) \sim \mathcal{N}_{\mathbb{C}}(\widetilde{z}_{\mathrm{card}}(t), \sigma_{\mathrm{card}}^2(t)),$$

where the stochastic magnitude $A(t) = |\widetilde{Z}_{\mathrm{card}}(t)|$ reflects beat-to-beat variability. Training employs the standard $\beta$-VAE loss, balancing $\ell_2$ reconstruction error against KL-divergence regularization:

$$\min_{W_E, W_D}\; \mathbb{E}_{Q,c}\Bigl[\,\bigl\|\,Q(t)-D(f(z(t)), c(t); W_D)\bigr\|_2^2\Bigr] + \beta\, \mathrm{KL}\Bigl[q(z|Q,c)\|\mathcal{N}(0,I)\Bigr].$$

No additional spatial regularizers are applied; improvements in SNR and artifact suppression result exclusively from the learned temporal subspace (Fang et al., 22 Nov 2025).

4. Unified Gated and Real-Time Generation

Post-training, the decoder $D(\cdot; W_D)$ operates at arbitrary locations in the continuous complex-harmonic space. Two principal reconstruction modes are supported:

Real-time playback: Employs the full stochastic latent trajectory (i.e., $\widetilde{Z}_{\mathrm{card}}(t)$ and $Z_{\mathrm{resp}}(t)$), with actual sequence timing, producing movies where each heartbeat is individually resolved with true amplitude variation:

$$A_{\mathrm{RT}}(x, t) = [u(x)]^T D(\widetilde{Z}_{\mathrm{card}}(t), Z_{\mathrm{resp}}(t), c(t)).$$

Gated cine reconstruction: Selects an archetypal amplitude $A_0$ and synthesizes phase-resolved images at $M$ phases by stepping through $\phi_m = 2\pi m / M$, holding respiration and contrast fixed:

$$A_{\mathrm{gate}}(x, \phi_m) = [u(x)]^T D(A_0 e^{i \phi_m}, Z_{\mathrm{resp}} = \bar{Z}, c = \bar{c}).$$

This approach enables both phase-resolved and beat-by-beat series from the same scan, spanning conventional gating and real-time imaging regimes (Fang et al., 22 Nov 2025).

5. Implementation and Artifact Suppression

Encoder and decoder architectures are fully-connected multilayer perceptrons (encoder: [25→50→100→70], decoder reversed), trained scan-specifically via Adam with learning rate $10^{-3}$. Cardiac and respiratory channels are disentangled by applying fixed FIR filters (respiratory: low-pass <0.67 Hz; cardiac: band-pass 0.67–2.5 Hz). During inference, artifact suppression is achieved by substituting $k[t-\mathrm{TR}]$ with a constant self-gating angle $k_{\mathrm{SG}}$, yielding an eddy-current-corrected basis:

$$\hat{D}(\widetilde{Z}(t), c_{\mathrm{fix}}) = D(\widetilde{Z}(t), c(t)|_{k[t-\mathrm{TR}]=k_{\mathrm{SG}}}).$$

This conditioning approach abolishes high-frequency peaks at golden-angle harmonics without smoothing physiologic high-frequency cardiac motion. In quantitative T1/T2 mapping, this implicit temporal denoising yields a two-fold reduction in intraseptal coefficient of variation (CoV) compared to conventional Multitasking (T1: 0.13 vs. 0.31; T2: 0.12 vs. 0.32; $p < 0.001$), with no added spatial smoothing (Fang et al., 22 Nov 2025).

6. Practical Impact and Future Directions

Generative Multitasking enables unified reconstruction of cine, multicontrast, and quantitative images from a single, undifferentiated free-breathing, non-ECG scan. It obviates the need for separate gated and real-time acquisitions, providing a flexible platform for cardiac motion representation, artifact suppression, and robust SNR enhancement. This framework can be extended to other acquisition settings and motion types by generalizing its conditioning and latent space definitions. A plausible implication is the potential for quantitative mapping protocols that are both motion-robust and artifact-suppressed without posthoc spatial regularization. Future work will likely investigate scaling, multispecies adaptation, cross-contrast generalization, and further integration with physiologic models (Fang et al., 22 Nov 2025).