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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. [ABSTRACT FROM AUTHOR]

Background: Unrolled neural networks (NNs) have been extensively applied to different image reconstruction problems across all imaging modalities. A key component of the latter is that they allow for physics‐informed learning of the regularization method, which is parametrized by the NN. However, due to the lack of understanding of deep NNs from a theoretical point of view, unrolled NNs are still black‐boxes when the regularizers are given by deep NNs, for example, U‐Nets. Purpose: Dictionarylearning (DL) is a well‐established regularization method, which is based on learning a transform to sparsely approximate the signals of interest. Typically, DL‐based image reconstruction either employs a dictionary, which was pretrained on a set of patches which were extracted from ground‐truth images or a dictionary which is jointly trained during the reconstruction. However, in both cases, the used DL‐algorithms are not designed to take into account the reconstruction problem or the underlying physical model, which describes the imaging process. In this work, we propose a DL‐algorithm based on unrolled NNs to overcome these limitations. Methods: We construct an unrolled NN, which corresponds to an unrolled DL‐based reconstruction algorithm and train the unrolled NN to optimize its weights, that is, the atoms of the dictionary, by back‐propagation in a supervised manner. Further, we propose a new way to employ a 2D dictionary in the spatio‐temporal domain. We tested and evaluated the method on an accelerated cardiac cine MR image reconstruction problem using 216/36/36 dynamic images for training, validation, and testing and compared it to two well‐known state‐of‐the‐art approaches for cardiac cine MRI based on deep iterative CNNs. Further, we analyze the obtained dictionaries in terms of dictionary‐coherence and structure of the atoms. Last, we compare the reported methods in terms of stability by applying them to an entirely different dataset consisting of 49 different test images. Results: The investigated physics‐informed DL‐approach yields significantly more accurate reconstructions compared to the DL‐method, which uses dictionaries obtained by decoupled pretraining, thereby providing an improvement of up to 4.90 dB in terms of PSNR and 5% in terms of SSIM. Further, the proposed spatio‐temporal 2D dictionary outperforms the 1D and 3D dictionaries by preventing smoothing of image details while still accurately removing undersampling artifacts and noise resulting in an increase of up to 1.10 dB in terms of PSNR and 4% in terms of SSIM. Although being surpassed by the CNNs on the first dataset, the proposed NNs‐based DL method is more stable compared to the latter approach and yields comparable results on the second dataset. Last, it has the advantage of being entirely interpretable in each component. Conclusions: The presented physics‐informed NN can be used as training algorithm for a classical and interpretable data‐driven regularization method based on a learned dictionary, which can then not only be linked to the considered data but also to the reconstruction method that the NN defines. [ABSTRACT FROM AUTHOR]