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Purpose: In the past, dictionary learning (DL) and sparse coding (SC) have been proposed for the regularization of image reconstruction problems. The regularization is given by a sparse approximation of all image patches using a learned dictionary, that is, an overcomplete set of basis functions learned from data. Despite its competitiveness, DL and SC require the tuning of two essential hyperparameters: the sparsity level S — the number of basis functions of the dictionary, called atoms, which are used to approximate each patch, and K — the overall number of such atoms in the dictionary. These two hyperparameters usually have to be chosen a priori and are determined by repetitive and computationally expensive experiments. Furthermore, the final reported values vary depending on the specific situation. As a result, the clinical application of the method is limited, as standardized reconstruction protocols have to be used. Methods: In this work, we use adaptive DL and propose a novel adaptive sparse coding algorithm for two‐dimensional (2D) radial cine MR image reconstruction. Using adaptive DL and adaptive SC, the optimal dictionary size K as well as the optimal sparsity level S are chosen dependent on the considered data. Results: Our three main results are the following: First, adaptive DL and adaptive SC deliver results which are comparable or better than the most widely used nonadaptive version of DL and SC. Second, the time needed for the regularization is accelerated due to the fact that the sparsity level S is never overestimated. Finally, the a priori choice of S and K is no longer needed but is optimally chosen dependent on the data under consideration. Conclusions: Adaptive DL and adaptive SC can highly facilitate the application of DL‐ and SC‐based regularization methods. While in this work we focused on 2D radial cine MR image reconstruction, we expect the method to be applicable to different imaging modalities as well. [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]

In dynamic magnetic resonance imaging (MRI) studies, the motion kinetics or the contrast variability are often hard to predict, hampering an appropriate choice of the image update rate or the temporal resolution. A constant azimuthal profile spacing (111.246°), based on the Golden Ratio, is investigated as optimal for image reconstruction from an arbitrary number of profiles in radial MRI. The profile order is evaluated and compared with a uniform profile distribution in terms of signal-to-noise ratio (SNR) and artifact level. The favorable characteristics of such a profile order are exemplified in two applications on healthy volunteers. First, an advanced sliding window reconstruction scheme is applied to dynamic cardiac imaging, with a reconstruction window that can be flexibly adjusted according to the extent of cardiac motion that is acceptable. Second, a contrast-enhancing k-space filter is presented that permits reconstructing an arbitrary number of images at arbitrary time points from one raw data set. The filter was utilized to depict the T1-relaxation in the brain after a single inversion prepulse. While a uniform profile distribution with a constant angle increment is optimal for a fixed and predetermined number of profiles, a profile distribution based on the Golden Ratio proved to be an appropriate solution for an arbitrary number of profiles. [ABSTRACT FROM AUTHOR]

Purpose: Iterative convolutional neural networks (CNNs) which resemble unrolled learned iterative schemes have shown to consistently deliver state‐of‐the‐art results for image reconstruction problems across different imaging modalities. However, because these methods include the forward model in the architecture, their applicability is often restricted to either relatively small reconstruction problems or to problems with operators which are computationally cheap to compute. As a consequence, they have not been applied to dynamic non‐Cartesian multi‐coil reconstruction problems so far. Methods: In this work, we propose a CNN architecture for image reconstruction of accelerated 2D radial cine MRI with multiple receiver coils. The network is based on a computationally light CNN component and a subsequent conjugate gradient (CG) method which can be jointly trained end‐to‐end using an efficient training strategy. We investigate the proposed training strategy and compare our method with other well‐known reconstruction techniques with learned and non‐learned regularization methods. Results: Our proposed method outperforms all other methods based on non‐learned regularization. Further, it performs similar or better than a CNN‐based method employing a 3D U‐Net and a method using adaptive dictionary learning. In addition, we empirically demonstrate that even by training the network with only iteration, it is possible to increase the length of the network at test time and further improve the results. Conclusions: End‐to‐end training allows to highly reduce the number of trainable parameters of and stabilize the reconstruction network. Further, because it is possible to change the length of the network at the test time, the need to find a compromise between the complexity of the CNN‐block and the number of iterations in each CG‐block becomes irrelevant. [ABSTRACT FROM AUTHOR]

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]

In this work we reduce undersampling artefacts in two-dimensional (2D) golden-angle radial cine cardiac MRI by applying a modified version of the U-net. The network is trained on 2D spatio-temporal slices which are previously extracted from the image sequences. We compare our approach to two 2D and a 3D deep learning-based post processing methods, three iterative reconstruction methods and two recently proposed methods for dynamic cardiac MRI based on 2D and 3D cascaded networks. Our method outperforms the 2D spatially trained U-net and the 2D spatio-temporal U-net. Compared to the 3D spatio-temporal U-net, our method delivers comparable results, but requiring shorter training times and less training data. Compared to the compressed sensing-based methods kt-FOCUSS and a total variation regularized reconstruction approach, our method improves image quality with respect to all reported metrics. Further, it achieves competitive results when compared to the iterative reconstruction method based on adaptive regularization with dictionary learning and total variation and when compared to the methods based on cascaded networks, while only requiring a small fraction of the computational and training time. A persistent homology analysis demonstrates that the data manifold of the spatio-temporal domain has a lower complexity than the one of the spatial domain and therefore, the learning of a projection-like mapping is facilitated. Even when trained on only one single subject without data-augmentation, our approach yields results which are similar to the ones obtained on a large training dataset. This makes the method particularly suitable for training a network on limited training data. Finally, in contrast to the spatial 2D U-net, our proposed method is shown to be naturally robust with respect to image rotation in image space and almost achieves rotation-equivariance where neither data-augmentation nor a particular network design are required. [ABSTRACT FROM AUTHOR]

A barrier to the adoption of non-Cartesian parallel magnetic resonance imaging for real-time applications has been the times required for the image reconstructions. These times have exceeded the underlying acquisition time thus preventing real-time display of the acquired images. We present a reconstruction algorithm for commodity graphics hardware (GPUs) to enable real time reconstruction of sensitivity encoded radial imaging (radial SENSE). We demonstrate that a radial profile order based on the golden ratio facilitates reconstruction from an arbitrary number of profiles. This allows the temporal resolution to be adjusted on the fly. A user adaptable regularization term is also included and, particularly for highly undersampled data, used to interactively improve the reconstruction quality. Each reconstruction is fully self-contained from the profile stream, i.e., the required coil sensitivity profiles, sampling density compensation weights, regularization terms, and noise estimates are computed in real-time from the acquisition data itself. The reconstruction implementation is verified using a steady state free precession (SSFP) pulse sequence and quantitatively evaluated. Three applications are demonstrated; real-time imaging with real-time SENSE 1) or k-t SENSE 2) reconstructions, and 3) offline reconstruction with interactive adjustment of reconstruction settings. [ABSTRACT FROM AUTHOR]

Simultaneous positron-emission tomography (PET)-magnetic resonance (MR) imaging is a hybrid technique in oncological hepatic imaging combining soft-tissue and functional contrast of dynamic contrast enhanced MR (DCE-MR) with metabolic information from PET. In this context, respiratory motion represents a major challenge by introducing blurring, artifacts and misregistration in the liver. In this work, we propose a free-breathing 3D non-rigid respiratory motion correction framework for simultaneously acquired DCE-MR and PET data, which makes use of higher spatial resolution MR data to derive motion information used directly during image reconstruction to minimize image blurring and motion artifacts. The main aim was to increase contrast of hepatic metastases to improve their detection and characterization. DCE-MR data were acquired at 3T through a golden radial phase encoding scheme, enabling derivation of motion fields. These were used in the motion compensated image reconstruction of DCE-MR time-series (48 time-points, 6 s temporal resolution, 1.5 mm isotropic spatial resolution) and 3D PET activity map, which was subsequently interpolated to the DCE-MR resolution. The extended Tofts model was fitted to DCE-MR data, obtaining functional parametric maps related to perfusion such as the endothelial permeability (). Fifty-seven hepatic metastases were identified and analyzed. Quantitative evaluations of motion correction in PET images demonstrated average percentage increases of 16% ± 5% (mean ± SD) in Contrast (C), 18% ± 6% in SUVmean and 14% ± 2% in SUVmax, while DCE-MR and scored contrast-to-noise-ratio increases of 64% ± 3% and 90% ± 6%, respectively. Motion-corrected data visually showed improved image contrast of hepatic metastases and effectively reduced blurring and motion artefacts. Scatter plots of SUVmean versus suggested that the proposed framework improved differentiation of measurements. The presented motion correction framework for simultaneously acquired PET-DCE-MR data provides accurately aligned images with increased contrast of hepatic lesions allowing for improved detection and characterization. [ABSTRACT FROM AUTHOR]

This paper presents a simulation framework for dynamic PET-MR. The main focus of this framework is to provide motion-resolved MR and PET data and ground truth motion information. This can be used in the optimisation and quantitative evaluation of image registration and in assessing the error propagation due to inaccuracies in motion estimation in complex motion-compensated reconstruction algorithms. Contrast and tracer kinetics can also be simulated and are available as ground truth information. To closely emulate medical examination, input and output of the simulation are files in standardised open-source raw data formats. This enables the use of existing raw data as a template input and ensures seamless integration of the output into existing reconstruction pipelines. The proposed framework was validated in PET-MR and image registration applications. It was used to simulate a FDG-PET-MR scan with cardiac and respiratory motion. Ground truth motion information could be utilised to optimise parameters for PET and synergistic PET-MR image registration. In addition, a free-breathing dynamic contrast enhancement (DCE) abdominal scan of a patient with hepatic lesions was simulated. In order to correct for breathing motion, a motion-corrected image reconstruction scheme was used and a Toft's model was fit to the DCE data to obtain quantitative DCE-MRI parameters. Utilising the ground truth motion information, the dependency of quantitative DCE-MR images on the accuracy of the motion estimation was evaluated. We demonstrated that respiratory motion had to be available with an average accuracy of at least the spatial resolution of the DCE-MR images in order to ensure an improvement in lesions visualisation and quantification compared to no motion correction. The proposed framework provides a valuable tool with a wide range of scientific PET and MR applications and will be available as part of the open-source project Synergistic Image Reconstruction Framework (SIRF). [ABSTRACT FROM AUTHOR]

We demonstrate a new method to recover 4D blood flow over the entire ventricle from partial blood velocity measurements using multiple 3D+t colour Doppler images and ventricular wall motion estimated using 3D+t BMode images. We apply our approach to realistic simulated data to ascertain the ability of the method to deal with incomplete data, as typically happens in clinical practice. Experiments using synthetic data show that the use of wall motion improves velocity reconstruction, shows more accurate flow patterns and improves mean accuracy particularly when coverage of the ventricle is poor. The method was applied to patient data from 6 congenital cases, producing results consistent with the simulations. The use of wall motion produced more plausible flow patterns and reduced the reconstruction error in all patients. [ABSTRACT FROM AUTHOR]

We have carried out a PET performance evaluation a silicon photo-multiplier (SiPM) based PET scanner designed for fully simultaneous pre-clinical PET/MR studies. The PET scanner has an inner diameter of 20 cm with an LYSO crystal size of 1.3 by 1.3 by 10 mm. The axial PET field of view (FOV) is 30.2 mm. The PET detector modules, which incorporate SiPMs, have been designed to be MR-compatible allowing them to be located directly within a Philips Achieva 3T MR scanner. The spatial resolution of the system measured using a point source in a non-active background, is just under 2.3 mm full width at half maximum (FWHM) in the transaxial direction when single slice rebinning (SSRB) and 2D filtered back-projection (FBP) is used for reconstruction, and 1.3 mm FWHM when resolution modeling is employed. The system sensitivity is 0.6% for a point source at the center of the FOV. The true coincidence count rate shows no sign of saturating at 30 MBq, at which point the randoms fraction is 8.2%, and the scatter fraction for a rat sized object is approximately 23%. Artifact-free images of phantoms have been obtained using FBP and iterative reconstructions. The performance is currently limited because only one of three axial ring positions is populated with detectors, and due to limitations of the first-generation detector readout ASIC used in the system. The performance of the system as described is sufficient for simultaneous PET-MR imaging of rat-sized animals and large organs within the mouse. This is demonstrated with dynamic PET and MR data acquired simultaneously from a mouse injected with a dual-labeled PET/MR probe. [ABSTRACT FROM PUBLISHER]

Highlights: [•] A new 3D velocity recovery method from 3+registered Doppler images is presented. [•] Variations in Doppler images are simulated with a new multiscale noise model. [•] We carry out a sensitivity analysis to view angles, noise and registration errors. [•] Error in volume on 3 volunteers agree with predicted error from simulation studies. [•] Preliminary results on three patients are accurate and capture complex flow patterns. [Copyright &y& Elsevier]

In hybrid PET/MR systems, attenuation maps can be derived from MR to correct for attenuation in PET. However, MR-based attenuation correction (AC) in abdominal applications remains challenging (i) because of poor signal from important tissue types in common MR sequences (e.g., cortical bone) and (ii) because of respiratory motion which results in misalignments between the derived attenuation maps and the PET emissions. Furthermore, respiratory motion also leads to motion-blurring artefacts in the final PET reconstructions. In this paper, we compute an MR-based 4D attenuation map including cortical bone by combining an Ultrashort Echo Time (UTE) acquisition with a subject-specific motion model derived from a second near real-time 3D MR image acquisition. This model allows us to create attenuation maps at any respiratory position which are used for AC in the reconstruction of different respiratory resolved PET images. The inverse of the model is used for motion compensation (MC) of these images. We demonstrate our approach on MR data from 5 healthy volunteers including 3 manually inserted artificial lesions. The impact of bone tissue and respiratory motion on AC is investigated in PET simulations (i) by misclassifying bone to soft tissue in the attenuation maps leading to errors of up to 26.0% in mean uptake for lesions close to bone, and (ii) by using a non-moving attenuation map leading to errors of up to 24.2%. The impact of respiratory motion on MC showed errors of up to 50.7% in areas of strong motion if MC was not performed. The results show that the effect of motion has to be considered both for attenuation correction and for motion-compensating PET emissions. This additive effect of motion is larger than the effect of a wrong AC. [ABSTRACT FROM PUBLISHER]