For fast data acquisition and low-delay reconstruction in applications using stack-of-stars trajectory, the authors propose a new reconstruction method using a CNN with temporal multiresolution inputs. Conventionally, stack-of-stars images reconstructed from a few spokes contain streaking artifacts. By utilizing view sharing technique for suppressing the artifacts, reconstructed images are often blurred. For low-delay reconstruction, it is not straightforward to use well-studied methods based on compressed sensing with temporal priors. The proposed method aims to adjust spatio-temporal resolution to a suitable one. Experimental results show that the proposed method could reconstruct highly under-sampled radial dynamic images with reduced artifacts.
Fast data acquisition and low-delay reconstruction are fundamental requirements for clinical use of dynamic MRI applications. For fast data acquisition, stack of 2D golden-angle radial trajectories, also known as stack-of-stars trajectory, is a popular method due to its motion robust properties. For reconstructing k-space data acquired with stack-of-stars trajectory, methods using compressed sensing with temporal priors1 have been extensively studied. However, these methods are not suitable for a low-delay reconstruction since evaluation of temporal priors requires many frames (e.g. an entire series of dynamic images).
For low-delay reconstruction, a method using a CNN that utilizes neighboring frames2 has been proposed earlier. While the quality of reconstructed images was better than single-frame solutions, it can be further improved.
The authors propose a new reconstruction method using a CNN whose inputs are temporal multiresolution images. As shown in Fig. 1, the proposed method reconstructs view-sharing images whose view-sharing factors are 1, 2, …, M as inputs of the CNN.
In dynamic imaging, there is an inherent trade-off between temporal and spatial resolution. To improve temporal resolution, typically stack-of-stars data are acquired with reduced number of spokes. However, these under-sampled images suffer from artifacts. By utilizing view sharing technique for suppressing the artifacts, reconstructed images are often blurred. Existing view-sharing techniques adjust temporal resolution by trial-and-error3. The proposed method aims to adjust temporal resolution to a suitable one.
The proposed method reconstructs a single image from consecutive N frames which includes past and future $$$(N-1)/2$$$ frames. Dynamic images are reconstructed in a frame-by-frame manner. To minimize time delay of reconstruction, first each input image is reconstructed using a (non-iterative) gridding algorithm. Then this image is fed into a CNN. The proposed CNN consists of convolution layers, rectified linear units (ReLUs) and dense connections4 as shown in Fig. 2. The CNN was trained by adaptive moment estimation (Adam)5 with a mean-squared-error loss function. The number of epochs was 100. The parameters of Adam were $$$\alpha=0.001$$$, $$$\beta_1=0.9$$$ and $$$\beta_2=0.999$$$.
For the cases of 13, 21, and 34 spokes per frame, the proposed method was compared with conventional methods using a CNN from a frame to a frame (1-to-1) and a CNN from 5 frames to a frame (5-to-1)2. In all experiments, the proposed method used 5 consecutive frames from 5 neighboring slices, i.e. $$$M=5$$$ and $$$N=5$$$.
For simulations, 8 volunteer images (7 training and 1 test image) were acquired with 3-dimensional fast spoiled gradient echo, T1-weighting, Cartesian trajectory, $$$256 \times 256 \times 32$$$, 24 frames and additional navigator signals. They were sorted retrospectively using the navigator signals and reconstructed as dynamic ground-truth images. A set of k-space data was simulated by applying a non-uniform FFT with a stack-of-stars trajectory to the dynamic ground-truth images.
For evaluating the proposed method with actual stack-of-stars data, 7 volunteer images (6 training and 1 testing images) were acquired with 3-dimensional fast spoiled gradient echo, T1-weighting, a stack-of-stars trajectory with 256 readout points and 32-40 slice encodes. For each volunteer, 3000-4000 spokes were acquired. They were reconstructed as both dynamic images with 13, 21, and 34 spokes per frame and a single ground-truth image.
The results showed that the proposed method reconstructed dynamic images with reconstruction delay of 2 ($$$=(N-1)/2$$$) future frames and processing time using gridding reconstruction of 5 ($$$=N$$$) images ($$$N(N+1)/2$$$ images for the first frame).
For evaluation using actual stack-of-stars data, the CNN was trained as a map from all dynamic images in a slice to a single ground-truth image in the slice. Evaluation using dynamic ground-truth images needs an acquisition with a high temporal resolution and is considered as a future work.
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