Synopsis

Keywords: Image Reconstruction, Heart

Neural fields cardiac MRI (NF-cMRI), a method for highly accelerated CINE reconstruction using deep learning, is proposed. NF-cMRI relies on an intensity network, based on neural fields with Fourier features to encode a continuous reconstruction. The network is trained with one undersampled radial k-space data set without the need of a fully-sampled reference image. Good image quality of the heart is achieved with 8 radial spokes/cardiac frame. Results are compared against GRASP. Future work will focus on reducing reconstruction time and evaluating the proposed approach in prospectively undersampled k-space data.

Introduction

Cardiac CINE MRI is the gold standard for cardiac functional assessment. However, spatial and temporal resolution is still limited since acquisition needs to be performed during one breath-hold (~15s). Several methods have been proposed that undersample the acquisition and exploit spatial-temporal redundancies to recover the non-acquired data ^1,2. More recently deep-learning based undersampled reconstruction with unrolled neural networks have been proposed to further accelerate the scan ³. These models usually rely on convolutional neural networks (CNNs), generative models (GANs) or variational autoencoders architectures (VAE), which need to consider non-uniform FFT (NUFFT) for the case of non-Cartesian acquisition to reconstruct a discrete image in space and time. Here we propose an alternative approach for highly accelerated radial cardiac CINE MRI using neural fields (NF-cMRI), without the need of NUFFT. The proposed approach relies on an intensity network, based on neural fields with Fourier features ⁴, which is trained by comparing the predicted image and multiple-coil measured data in k-space using the continuous Radon transform. The proposed approach is trained independently for each undersampled dataset and does not require large datasets nor fully sampled reference for training.

Methods

The proposed NF-cMRI approach relies on an intensity network (Intensity-Net), based on neural fields with Fourier features, which is trained by comparing the predicted image and multiple-coil measured data in k-space, using the continuous Radon transform (Fig.1). The Intensity-Net predicts the complex intensity value of the cardiac CINE images at spatial-temporal coordinate $$$(X,t)$$$. A neural field is simply a neural network whose input is a coordinate $$$x$$$, and whose output $$$\mathcal{N}(x;\theta)$$$ corresponds to the value of the image intensity at x. A multilayer perceptron (MLP) is trained to estimate the intensity of the reconstructed image in a given pixel, using the spatio-temporal coordinates $$$(X,t)$$$ of the pixel as input. An image is then generated by evaluating the MLP on a grid of points $$$\{X_{i,j},t_k\}_{i,j,k}$$$. A high dimensional mapping of the coordinates is used as input to the MLP, a technique called Fourier Features ⁴, to avoid the natural spectral bias of the MLPs ⁵, which learns first the low frequency components and can result in blurred images. Thus, a Gaussian Fourier Features is applied on the spatial coordinates, depending on two hyper-parameters: the mapping size $$$m$$$ and frequency gate $$$\sigma$$$, while the time coordinate is mapped to enforce periodicity.

Training is done by comparing the k-space of the generated image with the acquired multiple-coil undersampled data using the Fourier-slice theorem, by calculating the FFT 1D of the Radon Transform of the generated image. For radial trajectories, comparison in k-space is usually done with NUFFT ⁶. Because of the continuous nature of Intensity-Net, here a rotation and interpolation are not necessary on the reconstructed image to calculate the Radon Transform; since the image can be evaluated directly in the rotated frame.The network is trained in one undersampled k-space data set without the need of a fully-sampled reference image. Reconstruction then corresponds with the training process; retraining is necessary to process a different data set.The proposed approach was evaluated in complex-value cardiac cine images with simulated multiple-coils and retrospective tiny golden radial undersampling. Acceleration factors of 13.3, 20, and 40 (w.r.t. fully sampled Cartesian), corresponding to 12, 8 and 4 radial spokes per cardiac phase, were studied. Results are compared against GRASP ⁶, using the BART ⁷ implementation.

Results and Discussion

Impact of Fourier Features hyper-parameters in the proposed NF-cMRI approach can be observed on Fig 2. Corresponding Structural Similarity Index Measure (SSIM) and Peak Signal to Noise Ratio (PSNR) in comparison to the fully-sampled referenced are also shown in Fig 2. Both parameters are used to control the band of frequencies that the Intensity-Net can learn. Small values of $$$\sigma$$$ result in blurred images. Based on those results, hyperparameters are chosen as $$$\sigma = 8.0$$$ and $$$m = 150$$$, and NF-cMRI is evaluated in comparison to GRASP for different numbers of radial spokes per frame. A spatial comparison can be seen in Fig 3, and a spatio-temporal one in Fig 4, whereas Fig 5 presents an animation of the reconstructed 2D CINE with the proposed NF-cMRI and GRASP for 8 spokes per frame. Both approaches show comparable results for 12 radial spokes/frame however blurring is introduced with GRASP for higher accelerations, whereas NF-cMRI achieves lower errors and comparable results to the fully sampled references for up to 8 radial spokes/frame.

Conclusion

We have proposed a highly accelerated radial cardiac CINE MRI approach. The proposed NF-cMRI approach relies on an intensity network, based on neural fields with Fourier features, to achieve good image quality with 8 radial spokes/cardiac frame. The network is trained in one undersampled k-space data set without the need of a fully-sampled reference image. Future work will focus on reducing reconstruction time and evaluating the proposed approach in prospectively undersampled k-space data.