Jingyuan Lyu^{1}, Yu Ding^{1}, Jiali Zhong^{2}, Zhongqi Zhang^{3}, Lele Zhao^{3}, Jian Xu^{1}, Qi Liu^{1}, Ruchen Peng^{2}, and Weiguo Zhang^{1}

The main goal is to design and implement a sampling and reconstruction strategy that enables full heart coverage in a single breath-hold, with a relatively high spatial resolution (2.5 × 2.5 mm^{2}) and temporal resolution (40 ms). The challenge in sampling pattern design is how to sample most efficiently. In this work, we present a 10 fold accelerated real‐time cardiac cine MRI pulse sequence using a combination of compressed sensing and parallel imaging.

The proposed sampling scheme, called VAriable spatial-temporal LAtin hypercube and echo-Sharing (VALAS), is based on constrained distribution of sample positions on a spatiotemporal grid. Sampling density along time has less statistical fluctuations on LHS (Shown in Fig. 1).In data acquisition, the k-space is continuous prospectively undersampled (Shown in Fig. 2) using a lookup table. The lookup table was generated using variable LHS, with the center k-space 4-fold accelerated, transition region 6-fold accelerated, and outer region 14-fold accelerated (Fig. 3). In reconstruction, adjacent phases share 4 k-space echo data in the outer region, which results in an equivalent 7-fold acceleration in the outer region. We further assume the dynamic CMR series to be sparse in the spatial and temporal total variation (TV) domain. As a result, the image recovery problem is calculated by the following optimization function:

$$$\bf{x} = \arg\min_{\bf{x}} \frac{1}{2} \sum_{j} ||\Omega\bf {F} S_j \bf{x} - d_j|| ^2 + \lambda_1||TV_s(\bf{x})||_1 + \lambda_2||TV_t(\bf{x})||_1 $$$

where the first term is the data consistency term, and the latter two terms are the sparsity constraints; $$$\Omega$$$ represents the undersampling operator, $$$\textbf{F}$$$ is the 2 dimensional fast Fourier transform, $$$S_j$$$ represents the *j*-th coil sensitivity profile, $$$d_j$$$ the undersampled k-space data from the *j*-th coil, and *j *counts all channels.

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Fig. 1. Illustration of LHS and variable density random sampling . Summations along time has less statistical fluctuation of LHS, than variable density random sampling.

Fig. 2. LHC Real-Time Cine Acquisition Pattern with Echo-Sharing

Fig. 3. Real-time
cardiac cine k-t sampling pattern using variable LHS with
echo sharing

Fig. 4. Reconstruction results from perspective undersampling

Fig. 5. Reconstructions from retrospective undersamplings
using VALAS (middle column), variable density random sampling (right column),
compared with the reference images (left column).