Data-efficient Bayesian learning for radial dynamic MR reconstruction.

BACKGROUND: Cardiac MRI has become the gold-standard imaging technique for assessing cardiovascular morphology and function. In spite of this, its slow data acquisition process presents imaging challenges due to the motion from heartbeats, respiration, and blood flow. In recent studies, deep learning (DL) algorithms have shown promising results for the task of image reconstruction. However, there have been instances where they have introduced artifacts that may be misinterpreted as pathologies or may obscure the detection of pathologies. Therefore, it is important to obtain a metric, such as the uncertainty of the network output, that identifies such artifacts. However, this can be quite challenging for large-scale image reconstruction problems such as dynamic multi-coil non-Cartesian MRI.

PURPOSE: To efficiently quantify uncertainties of a physics-informed DL-based image reconstruction method for a large-scale accelerated 2D multi-coil dynamic radial MRI reconstruction problem, and demonstrate the benefits of physics-informed DL over model-agnostic DL in reducing uncertainties while at the same time improving image quality.

METHODS: We extended a recently proposed physics-informed 2D U-Net that learns spatio-temporal slices (named XT-YT U-Net), and employed it for the task of uncertainty quantification (UQ) by using Monte Carlo dropout and a Gaussian negative log-likelihood loss function. Our data comprised 2D dynamic MR images acquired with a radial balanced steady-state free precession sequence. The XT-YT U-Net, which allows for training with a limited amount of data, was trained and validated on a dataset of 15 healthy volunteers, and further tested on data from four patients. An extensive comparison between physics-informed and model-agnostic neural networks (NNs) concerning the obtained image quality and uncertainty estimates was performed. Further, we employed calibration plots to assess the quality of the UQ.

RESULTS: The inclusion of the MR-physics model of data acquisition as a building block in the NN architecture led to higher image quality (NRMSE: - 33 ± 8.2 % $-33 \pm 8.2 \%$ , PSNR: 6.3 ± 1.3 % $6.3 \pm 1.3 \%$ , and SSIM: 1.9 ± 0.96 % $1.9 \pm 0.96 \%$ ), lower uncertainties ( - 46 ± 8.7 % $-46 \pm 8.7 \%$ ), and, based on the calibration plots, an improved UQ compared to its model-agnostic counterpart. Furthermore, the UQ information can be used to differentiate between anatomical structures (e.g., coronary arteries, ventricle boundaries) and artifacts.

CONCLUSIONS: Using an XT-YT U-Net, we were able to quantify uncertainties of a physics-informed NN for a high-dimensional and computationally demanding 2D multi-coil dynamic MR imaging problem. In addition to improving the image quality, embedding the acquisition model in the network architecture decreased the reconstruction uncertainties as well as quantitatively improved the UQ. The UQ provides additional information to assess the performance of different network approaches.