Accelerated Coronary MRI with sRAKI: A Database-Free Self-Consistent Neural Network k-space Reconstruction for Arbitrary Undersampling

This study aims to accelerate coronary MRI using a novel reconstruction algorithm, called self-consistent robust artificial-neural-networks for k-space interpolation (sRAKI). sRAKI performs iterative parallel imaging reconstruction by enforcing coil self-consistency using subject-specific neural networks. This approach extends the linear convolutions in SPIRiT to nonlinear interpolation using convolutional neural networks (CNNs). These CNNs are trained individually for each scan using the scan-specific autocalibrating signal (ACS) data. Reconstruction is performed by imposing the learned self-consistency and data-consistency enabling sRAKI to support random undersampling patterns. Fully-sampled targeted right coronary artery MRI was acquired in six healthy subjects for evaluation. The data were retrospectively undersampled, and reconstructed using SPIRiT, $\ell_1$-SPIRiT and sRAKI for acceleration rates of 2 to 5. Additionally, prospectively undersampled whole-heart coronary MRI was acquired to further evaluate performance. The results indicate that sRAKI reduces noise amplification and blurring artifacts compared with SPIRiT and $\ell_1$-SPIRiT, especially at high acceleration rates in targeted data. Quantitative analysis shows that sRAKI improves normalized mean-squared-error (~44% and ~21% over SPIRiT and $\ell_1$-SPIRiT at rate 5) and vessel sharpness (~10% and ~20% over SPIRiT and $\ell_1$-SPIRiT at rate 5). In addition, whole-heart data shows the sharpest coronary arteries when resolved using sRAKI, with 11% and 15% improvement in vessel sharpness over SPIRiT and $\ell_1$-SPIRiT, respectively. Thus, sRAKI is a database-free neural network-based reconstruction technique that may further accelerate coronary MRI with arbitrary undersampling patterns, while improving noise resilience over linear parallel imaging and image sharpness over $\ell_1$ regularization techniques.

💡 Research Summary

The paper introduces a novel reconstruction framework called self‑consistent robust artificial‑neural‑networks for k‑space interpolation (sRAKI) aimed at accelerating coronary magnetic resonance imaging (MRI). Conventional parallel imaging methods such as SPIRiT enforce coil self‑consistency using linear convolution kernels derived from autocalibrating signal (ACS) data. While effective for uniform undersampling, linear models are limited in handling arbitrary sampling patterns and are susceptible to noise amplification. Recent deep‑learning approaches mitigate some of these issues but typically require large external training databases, which are impractical for high‑resolution cardiac MRI where fully sampled reference data are difficult to acquire.

sRAKI circumvents these constraints by training a subject‑specific convolutional neural network (CNN) solely on the ACS region of each scan. The network architecture consists of four layers: an input layer with 5 × 5 kernels, two hidden layers with 3 × 3 kernels (16 and 8 feature maps respectively), and an output layer with 5 × 5 kernels that restores the original number of coil channels (2 × n_coils, after concatenating real and imaginary parts). Unlike the original RAKI method, which uses separate CNNs for each coil, sRAKI employs a single CNN that maps the multi‑coil k‑space onto itself, dramatically reducing computational load. Training minimizes a mean‑squared‑error loss using the Adam optimizer (learning rate 0.01, up to 1000 iterations).

During reconstruction, sRAKI solves the following optimization problem:

 minₓ ‖y − D x‖₂² + β ‖x − G(x)‖₂²,

where y denotes the acquired undersampled data, D the sampling operator, G the trained CNN, and β a weighting factor. To avoid manual tuning of β, the authors enforce strict data consistency as in SPIRiT: after each iteration, acquired k‑space points are overwritten with the measured values, and gradients are computed only for the missing points. The objective is minimized with Adam (learning rate 2), leveraging back‑propagation to obtain gradients with respect to the image variable x rather than the network parameters.

The method was evaluated on a 3 T Siemens Prisma scanner using a 30‑channel body coil. Six healthy volunteers underwent targeted right coronary artery (RCA) imaging (1 × 1 × 3 mm³ resolution). Fully sampled datasets were retrospectively undersampled with Poisson‑disc patterns at acceleration factors R = 2, 3, 4, 5. Additionally, a separate subject was prospectively scanned with whole‑heart coverage (1.2 mm isotropic) at R = 5. Reconstructions were compared against conventional SPIRiT (5 × 5 linear kernels) and ℓ₁‑SPIRiT (SPIRiT plus Daubechies wavelet sparsity, threshold = 0.0005).

Quantitative metrics included normalized mean‑squared error (NMSE) and normalized vessel sharpness (NVS). At R = 5, sRAKI reduced NMSE by ~44 % relative to SPIRiT and ~21 % relative to ℓ₁‑SPIRiT. Vessel sharpness improved by ~10 % over SPIRiT and ~20 % over ℓ₁‑SPIRiT. In whole‑heart data, sRAKI yielded NVS values of 0.30 (RCA) and 0.28 (LCX), compared with 0.25/0.22 for SPIRiT and ℓ₁‑SPIRiT, representing 11 %–15 % gains. Visual inspection confirmed markedly lower noise amplification and reduced blurring at high acceleration rates.

Key insights: (1) Training on scan‑specific ACS eliminates the need for large external datasets and automatically adapts to subject‑specific coil sensitivities and noise levels. (2) The nonlinear CNN captures complex coil interactions more effectively than linear SPIRiT kernels, leading to superior noise resilience. (3) By embedding the learned self‑consistency into an iterative data‑consistency framework, sRAKI supports arbitrary undersampling patterns, extending the applicability of RAKI beyond uniform undersampling.

Limitations include the relatively shallow network depth and reliance on a simple MSE loss; incorporating deeper architectures, perceptual or adversarial losses, and additional regularizers (e.g., total variation) could further improve performance, especially at even higher acceleration factors. Moreover, the current implementation operates on 2‑D slices after an inverse Fourier transform along the fully sampled phase‑encode direction; a fully 3‑D CNN could exploit correlations across all three spatial dimensions.

In conclusion, sRAKI presents a practical, database‑free deep‑learning reconstruction that bridges the gap between traditional linear parallel imaging and modern supervised deep‑learning methods. It delivers substantial reductions in noise and blurring while preserving vessel sharpness, making it a promising tool for clinically feasible, accelerated coronary MRI with flexible sampling strategies. Future work will focus on broader clinical validation, real‑time implementation, and exploration of advanced network designs to push acceleration limits further.