SCMR/ISMRM Co-Provided Workshop
SCMR 22nd Annual Scientific Sessions
Lengthy acquisition times remain a challenge in coronary MRI, necessitating improved imaging acceleration methods. Recently, a new technique called Robust Artificial-neural-networks for k-space Interpolation (RAKI) was proposed, which employs multi-layer convolutional neural networks (CNN) to nonlinearly interpolate missing k-space lines . However, this approach was limited to uniform undersampling patterns. In this study, we extend this technique to arbitrary undersampling patterns by employing the idea of self-consistency, as in SPIRiT . This new approach, called SPIRiT-RAKI, uses CNNs for self-consistency, while enforcing consistency with acquired data, and is implemented using a gradient descent approach.
A four-layer CNN architecture was designed to reconstruct multi-coil data (Fig. 1). The network had 2nc input/output channels (factor of 2: due to complex k-space being mapped to real field, nc: number of coils) with ReLU operations performed on all layers except the last one. The fully-sampled central ACS lines were used to train the network with mean squared error loss using the Adam optimizer. This CNN enforces self-consistency among coils, i.e. x = G(x) where x is the desired k-space data across all coils.
In addition to this self-consistency, the solution should also be consistent with the acquired data, y = Dx + n, where D is the undersampling operator in k-space and n is noise. Thus, the overall solution is obtained by minimizing ||y-Dx||22 + β||x-G(x)||22. Conjugate gradient (CG) used in  is not applicable here due to nonlinearity of G(∙), thus gradient-descent (GD) approach is utilized.
Targeted right coronary artery MRI was acquired at 3T with a 30-channel body-coil using a T2-prepared GRE sequence. The imaging parameters were: FOV=300×300×45mm3, resolution= 1×1×3mm3. A central 2D slice was undersampled at R=2 and 3 using uniform and random patterns, with an ACS region of 28 lines. SPIRiT using the online CG code  without sparsity regularization was also implemented for comparison.
The results of uniform undersampling in Fig. 2 indicate that the proposed SPIRiT-RAKI technique significantly suppressed the residual aliasing and blurring artifacts visible in the results of non-regularized SPIRiT. At higher rates (R=3) noise was visible for both methods. The NMSE for SPIRiT and SPIRiT-RAKI (for R = 2, 3) were: 0.100, 0.131 and 0.048, 0.070 respectively. Fig. 3 reveals similar reduction in aliasing and blurring artifacts for random undersampling. The NMSE for SPIRiT and SPIRiT-RAKI (for R=2, 3) were: 0.081, 0.106 and 0.051, 0.076 respectively.
The proposed SPIRiT-RAKI technique enables CNN-based parallel cardiac imaging with a scan-specific and database-free scheme for arbitrary k-space undersampling patterns. SPIRiT-RAKI utilizes a GD-based approach to enforce self-consistency among coils and data-consistency.