Introduction

RAKI [1] is a scan-specific k-space interpolation technique based on deep convolutional networks. RAKI bears superior noise resilience compared to GRAPPA [2], resulting in improved image quality. However, RAKI may introduce severe residual artefacts and blurring in conventional in-plane image reconstruction due to reduced number of autocalibration signal (ACS) lines at higher acceleration factors. In this work, we propose Gradual RAKI, where k-space segments are sequentially filled up with the interpolated data by subsequent RAKI reconstructions intermitted with a single GRAPPA reconstruction to mitigate RAKI-introduced blurring. This work has been conceived due to fruitful discussions on Iterative RAKI, which has been presented at the annual meeting of the ESMRMB 2021 congress [3].

Methods

Gradual RAKI consists of a few consecutive reconstruction steps only, that can be divided into a preparatory block and a robust RAKI block (Fig. 1). The former aims to generate synthetic ACS lines that can be fed to the latter as the final reconstruction step. The preparatory components of Gradual RAKI’s pipeline serve two distinct purposes, and thus are divided into two sections. First, two consecutive RAKI reconstructions are carried out to serve as initial data augmentation steps (i.e., synthetic ACS line generation). Due to its superior noise resilience compared to GRAPPA, RAKI is assigned as a preferable method for initial data augmentation to minimize noise propagation into the synthetic ACS data set. Second, beyond further increasing the synthetic ACS lines, a single GRAPPA reconstruction is performed to counterbalance the potentially RAKI-introduced residual artefacts and blurring, stemming from the low number of original ACS lines. As the final step of Gradual RAKI, a RAKI reconstruction synthesizes the missing lines of the whole accelerated measurement bearing a sufficient number of synthetic ACS lines originating from the preparatory block.

Rather than opting for a single robust neural network with sufficient number of ACS lines to adequately generalize for all frequency components, we designed Gradual RAKI’s consecutive reconstruction steps to remain within the range of their generalization capacity based on the extent of available k-space training data.

Each reconstruction output serves as training input for the consecutive step. Original ACS lines are reinserted after every reconstruction step. 4,6,8 ACS lines are assigned as excessively limited original training data for acceleration factor R = 2,3,4, respectively, i.e., 2 x acceleration factor as ACS lines. In the data augmentation phase of the preparatory block, the output size is selected to be 2 x acceleration factor greater than input size, thus the undersampled k-space is filled up symmetrically with respect to k-space origin. Complex-valued convolution [4][3] is implemented to involve correlation between real and imaginary parts representing k-space phase information. Complex ReLU [5] is chosen as activation and mean-squared-error (MSE) as loss function. The number of epochs is set to 300, with MSE normalized to the first iteration error dropping to 1e-4 as the early stopping condition. Learning rate is set to 3e-3 universally and training weights are randomly initialized in every case as all reconstruction steps are treated individually.

2D in vivo brain data were collected for evaluation with a 32-channel receiver coil on a clinical scanner on a healthy volunteer at 3 T (Magnetom Prisma, Siemens Healthineers, Erlangen, Germany). One set (ref. to as neuro_T1) was acquired using TSE with TR/TE = 350/2.46 ms, FOV = 220 x 193 mm², matrix size 256 x 224. Another set (ref. to as neuro_T2) was acquired using Inversion recovery TSE (FLAIR) with TR/TE = 9000/111 ms, FOV = 220 x 193 mm², matrix size 256 x 224.

Quantitative visual remarks and difference images are displayed with respect to the fully sampled reference data set. Normalized Mean Squared Error (NMSE), Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Metric (SSIM) computed with respect to the fully sampled reference data set serve as image quality metrics. GRAPPA and RAKI reconstructions are carried out from the original ACS lines to serve as comparison baseline.

Results

Gradual RAKI shows improved image quality compared to RAKI and GRAPPA at 4-fold acceleration even with 8 ACS lines as excessively limited original training data. (Fig. 2 and Fig. 3). Image quality metrics demonstrate the performance of Gradual RAKI compared to GRAPPA and RAKI at 2,3,4-fold accelerations with the application of 4,6,8 ACS lines, respectively. (Fig. 4).

Discussion

Gradual RAKI exhibits the benefit of mixing RAKI and GRAPPA in a preparatory block for data augmentation purposes prior to a conventional RAKI reconstruction. Data augmentation provides an effective way to create synthetic ACS lines out of 8 ACS lines at 4-fold acceleration, while valuable features are retained from both RAKI and GRAPPA reconstruction methods.
In the original RAKI article of Akçakaya et al. [1], GRAPPA was proposed to generate synthetic ACS lines. However, in Gradual RAKI’s approach, an initial RAKI reconstruction was chosen for data augmentation purposes in the preparatory block and GRAPPA was only used as an intermittent step to mitigate RAKI-related artefacts.