CDI-Net: Joint Deep Learning for Cardiac SPECT

• CDI-Net is a deep learning framework that jointly denoises low-dose projections, recovers full-dose images from limited-angle data, and generates synthetic μ-maps.
• It integrates alternating U-Nets in projection and image domains with cross-domain residual and dense connections to iteratively refine outputs.
• Adaptive weight recalibrators enhance channel features, resulting in significant improvements in NMSE, SSIM, and PSNR over traditional methods.

Cross-Domain Iterative Networks (CDI-Net) are deep learning architectures designed for the simultaneous solution of multiple, clinically motivated inverse problems in medical imaging, particularly in cardiac Single-Photon Emission Computed Tomography (SPECT). CDI-Net is the first reported framework to address, within a unified end-to-end trainable network, (i) denoising of low-dose (LD) projections, (ii) full-angle, full-dose (FA–FD) projection reconstruction from limited-angle (LA) input, and (iii) CT-free attenuation correction (AC) via synthetic attenuation map ($\mu$-map) generation. CDI-Net achieves this through tightly integrated projection- and image-domain networks, cross-domain iterative connections, and adaptive channel-wise feature recalibration, resulting in significant improvements in projection, $\mu$-map, and reconstruction accuracy compared to prior methods addressing each task separately (Chen et al., 2023).

1. Motivation and Problem Formulation

Cardiac SPECT imaging routinely contends with multiple confounding factors: LD protocols, intended to reduce patient radiation burden, amplify Poisson noise in projection data; LA acquisitions, which limit detector coverage for reduced hardware cost and expedited scans, induce severe angular undersampling artifacts; and CT-derived $\mu$-maps, the standard for AC, are unavailable to most SPECT scanners and may introduce dose and misregistration issues. CDI-Net is developed to jointly address these limitations.

The SPECT projection model under monoenergetic assumptions is formalized as:

$$P = \mathbf{A}\lambda \odot \exp(-\mathbf{B}\mu) \,,$$

where $\lambda(x)$ represents the activity distribution, $\mu(x)$ the linear attenuation coefficients, $\mathbf{A}$ the emission system matrix, $\mathbf{B}$ the attenuation projection operator, and $\odot$ denotes element-wise multiplication.

CDI-Net operationalizes the joint denoising and LA-to-FA recovery and synthetic $\mu$-map generation as learning mappings:

$$\hat P_F = \mathcal{P}(P_L), \quad \hat \mu = \mathcal{I}(I_L, \cdot)$$

with $P_L$ the input 10%-count, 9-angle projection, $I_L$ the uncorrected ML-EM reconstruction from $P_L$, and $\hat{P}_F$, $\hat{\mu}$ the predicted FA–FD projection and $\mu$-map, respectively (Chen et al., 2023).

2. CDI-Net Architecture and Cross-Domain Iteration

CDI-Net comprises alternating pairs of U-Net architectures in projection space (“Proj-Net”) and image space (“Img-Net”), interleaved across up to $N=5$ iterative blocks. This alternation leverages two principal mechanisms:

• Cross-Domain Residual Connections (CD-RC): Emission (projection) and anatomical ($\mu$-map) cues are exchanged between domains. Specifically, ML-EM backprojection of predicted projections ($\mathcal{T}_b(\hat{P}_F^m)$) is concatenated with image-domain features; forward projection of $\mu$-maps ($\mathcal{T}_f(\hat{\mu}^m)$) informs the projection-domain network.
• Cross-Iteration Dense Connections (CI-DC): All intermediate estimates of projections and $\mu$-maps are concatenated with their respective domain inputs at each iteration, promoting iterative refinement.

After $N$ iterations, CDI-Net outputs both $\hat P_F^N$ and $\hat \mu^N$. These are supplied to a conventional off-line ML-EM algorithm (30 iterations) for final attenuation-corrected SPECT image reconstruction (Chen et al., 2023).

3. Adaptive Weight Recalibrators

Adaptive Weight Recalibrators (AWR) are channel-wise feature re-weighting modules applied prior to each U-Net in both domains. Each AWR module processes a multi-channel input tensor $$F_{Mul}=[f_1, ..., f_C] \in \mathbb{R}^{H \times W \times D \times C}$$ using global spatial average pooling, a two-layer fully-connected block, and sigmoid nonlinearity to yield channel scalars $\hat{\alpha}_i \in (0,1)^C$. Features are then rescaled ($$\hat{F}_{Chl} = [\hat{\alpha}_1 f_1, ..., \hat{\alpha}_C f_C]$$) and a global residual connection restores the original information:

$\hat F_{AWR} = \hat F_{Chl} + F_{Mul}$

AWR modules adaptively modulate, via data-driven learning, the impact of emission and anatomical feature channels on final predictions, significantly improving both projection and $\mu$-map estimation accuracy (Chen et al., 2023).

4. Training Paradigm and Loss Formulation

CDI-Net is optimized using an $L_1$ loss summed across $N=5$ projection and $\mu$-map prediction iterations:

$$\mathcal{L} = \sum_{i=1}^N \left[ w_P \|\hat{P}_F^i - P_F\|_1 + w_\mu \|\hat{\mu}^i - \mu\|_1 \right]$$

with $w_P = w_\mu = 0.5$. Adam optimization is employed (initial learning rates: $10^{-3}$ for image-domain, $10^{-4}$ for projection-domain; exponential decay). CDI-Net is trained for 50 epochs; single-task baselines (UNet, Attn-UNet, DuDoSS) are trained for 200 epochs (Chen et al., 2023).

5. Experimental Evaluation and Outcomes

Experiments are conducted on 474 clinical myocardial perfusion imaging (MPI) SPECT studies (GE NM/CT 570c, 19 pinhole detectors, 3 columns). The dataset is partitioned into 200 training, 74 validation, and 200 test subjects. Inputs are 10%-count, 9-angle LD–LA projections; ground truth is provided by FA–FD projections and registered CT $\mu$-maps.

Reconstruction accuracy is quantified by NMSE, NMAE, SSIM, and PSNR. CDI-Net demonstrates consistent, statistically significant performance gains over all baseline architectures:

Output	Metric	CDI-Net	Best Baseline
Pred. Projections	NMSE (%)	2.15 $\pm$ 0.69	3.19 $\pm$ 1.11
$\mu$-maps	NMSE (%)	11.42 $\pm$ 4.31	12.45
AC SPECT	NMSE (%)	4.82 $\pm$ 1.44	5.68
	SSIM (Recon)	0.8829 $\pm$ 0.0194	0.8706
	PSNR (Recon, dB)	32.69 $\pm$ 1.65	32.00

Improvements are significant ($p < 0.001$). Error curves (Figure 1 (Chen et al., 2023)) indicate stable convergence by iteration $N=5$, and robust superiority persists over varying LD levels from 1% to 80%.

6. Ablation Studies

Ablation studies isolate the contributions of dense cross-iteration aggregation (CI-DC), cross-domain feature fusion (CD-RC), and adaptive re-weighting (AWR). Removal of any component degrades performance. For example, omitting CI-DC increases projection NMSE to 2.56% (vs 2.15% full), $\mu$-NMSE to 11.88% (vs 11.42%), and AC SPECT NMSE to 5.45% (vs 4.82%). Analogous declines are observed for exclusion of CD-RC or AWR. This confirms the complementary roles of iterative and cross-domain information fusion and channel calibration (Chen et al., 2023).

7. Context and Impact

CDI-Net establishes a new paradigm in medical imaging deep learning by enabling simultaneous joint solution of denoising, LA-to-FA recovery, and pseudo–CT attenuation correction. The methodology integrates projection and image-domain cues, dense iterative fusion, and channel adaptivity in a fully end-to-end trainable framework. The demonstrated improvements in projection, $\mu$-map, and AC SPECT image quality on clinical data suggest enhanced clinical utility and generalizability relative to single-task and dual-domain approaches. CDI-Net’s design principles—cross-domain iterative coupling and channel recalibration—offer a template for expanding joint multi-task inverse solution networks in other imaging domains (Chen et al., 2023).