Deep neural networks have demonstrated promising potential for the field of medical image reconstruction, successfully generating high quality images for CT, PET and MRI. In this work, an MRI reconstruction algorithm, which is referred to as quantitative susceptibility mapping (QSM), has been developed using a deep neural network in order to perform dipole deconvolution, which restores magnetic susceptibility source from an MRI field map. Previous approaches of QSM require multiple orientation data (e.g. Calculation of Susceptibility through Multiple Orientation Sampling or COSMOS) or regularization terms (e.g. Truncated K-space Division or TKD; Morphology Enabled Dipole Inversion or MEDI) to solve an ill-conditioned dipole deconvolution problem. Unfortunately, they either entail challenges in data acquisition (i.e. long scan time and multiple head orientations) or suffer from image artifacts. To overcome these shortcomings, a deep neural network, which is referred to as QSMnet, is constructed to generate a high quality susceptibility source map from single orientation data. The network has a modified U-net structure and is trained using COSMOS QSM maps, which are considered as gold standard. Five head orientation datasets from five subjects were employed for patch-wise network training after doubling the training data using a model-based data augmentation. Seven additional datasets of five head orientation images (i.e. total 35 images) were used for validation (one dataset) and test (six datasets). The QSMnet maps of the test dataset were compared with the maps from TKD and MEDI for their image quality and consistency with respect to multiple head orientations. Quantitative and qualitative image quality comparisons demonstrate that the QSMnet results have superior image quality to those of TKD or MEDI results and have comparable image quality to those of COSMOS. Additionally, QSMnet maps reveal substantially better consistency across the multiple head orientation data than those from TKD or MEDI. As a preliminary application, the network was further tested for three patients, one with microbleed, another with multiple sclerosis lesions, and the third with hemorrhage. The QSMnet maps showed similar lesion contrasts with those from MEDI, demonstrating potential for future applications.

Purpose We introduce L2-regularized reconstruction algorithms with closed-form solutions that achieve dramatic computational speed-up relative to state of the art L1- and L2-based iterative algorithms while maintaining similar image quality for various applications in MRI reconstruction. Materials and Methods We compare fast L2-based methods to state of the art algorithms employing iterative L1- and L2-regularization in numerical phantom and in vivo data in three applications; 1) Fast Quantitative Susceptibility Mapping (QSD), 2) Lipid artifact suppression in Magnetic Resonance Spectroscopic Imaging (MRSI), and 3) Diffusion Spectrum Imaging (DSI). In all cases, proposed L2-based methods are compared with the state of the art algorithms, and two to three orders of magnitude speed up is demonstrated with similar reconstruction quality. Results The closed-form solution developed for regularized QSM allows processing of a 3D volume under 5 seconds, the proposed lipid suppression algorithm takes under 1 second to reconstruct single-slice MRSI data, while the PCA based DSI algorithm estimates diffusion propagators from undersampled q-space for a single slice under 30 seconds, all running in Matlab using a standard workstation. Conclusion For the applications considered herein, closed-form L2-regularization can be a faster alternative to its iterative counterpart or L1-based iterative algorithms, without compromising image quality.

Quantitative Susceptibility Mapping (QSM) estimates the underlying tissue magnetic susceptibility from the gradient echo (GRE) phase signal through background phase removal and dipole inversion steps. Each of these steps typically requires solving an ill-posed inverse problem and thus necessitates additional regularization. Recently developed single-step QSM algorithms directly relate the unprocessed GRE phase to the unknown susceptibility distribution, thereby requiring the solution of a single inverse problem. In this work, we show that such a holistic approach provides susceptibility estimation with artifact mitigation and develop efficient algorithms that involve simple analytical solutions for all of the optimization steps. Our methods employ Total Variation (TV) and Total Generalized Variation (TGV) to jointly perform the background removal and dipole inversion in a single step. Using multiple spherical mean value (SMV) kernels of varying radii permits high fidelity background removal while retaining the phase information in the cortex. Using numerical simulations, we demonstrate that the proposed single-step methods reduce the reconstruction error by up to 66% relative to the multi-step methods that involve SMV background filtering with the same number of SMV kernels, followed by TV- or TGV-regularized dipole inversion. In vivo single-step experiments demonstrate a dramatic reduction in dipole streaking artifacts and improved homogeneity of image contrast. These acquisitions employ the rapid 3D-EPI and the Wave-CAIPI trajectories for SNR-efficient whole-brain imaging. Herein, we also demonstrate the Multi-Echo capability of Wave-CAIPI sequence for the first time, and introduce an automated, phase-sensitive coil sensitivity estimation scheme based on a 4-second calibration acquisition.

Purpose To introduce a combined machine learning (ML)‐ and physics‐based image reconstruction framework that enables navigator‐free, highly accelerated multishot echo planar imaging (msEPI) and demonstrate its application in high‐resolution structural and diffusion imaging. Methods Single‐shot EPI is an efficient encoding technique, but does not lend itself well to high‐resolution imaging because of severe distortion artifacts and blurring. Although msEPI can mitigate these artifacts, high‐quality msEPI has been elusive because of phase mismatch arising from shot‐to‐shot variations which preclude the combination of the multiple‐shot data into a single image. We utilize deep learning to obtain an interim image with minimal artifacts, which permits estimation of image phase variations attributed to shot‐to‐shot changes. These variations are then included in a joint virtual coil sensitivity encoding (JVC‐SENSE) reconstruction to utilize data from all shots and improve upon the ML solution. Results Our combined ML + physics approach enabled Rinplane × multiband (MB) = 8‐ × 2‐fold acceleration using 2 EPI shots for multiecho imaging, so that whole‐brain T2 and T2* parameter maps could be derived from an 8.3‐second acquisition at 1 × 1 × 3‐mm3 resolution. This has also allowed high‐resolution diffusion imaging with high geometrical fidelity using 5 shots at Rinplane × MB = 9‐ × 2‐fold acceleration. To make these possible, we extended the state‐of‐the‐art MUSSELS reconstruction technique to simultaneous multislice encoding and used it as an input to our ML network. Conclusion Combination of ML and JVC‐SENSE enabled navigator‐free msEPI at higher accelerations than previously possible while using fewer shots, with reduced vulnerability to poor generalizability and poor acceptance of end‐to‐end ML approaches.

Abbreviations:• CNN: convolutional neural network • MEDI: morphology enabled dipole inversion • NDI: nonlinear dipole inversion • QSM: quantitative susceptibility mapping • SMV: spherical mean value • TGV: total generalized variation • TKD: truncated k-space division • TV: total variation • VaNDI: variational nonlinear dipole inversion • VN: variational network • w.r.t: with respect to Abstract We propose Nonlinear Dipole Inversion (NDI) for high-quality Quantitative Susceptibility Mapping (QSM) without regularization tuning, while matching the image quality of state-of-the-art reconstruction techniques. In addition to avoiding over-smoothing that these techniques often suffer from, we also obviate the need for parameter selection. NDI is flexible enough to allow for reconstruction from an arbitrary number of head orientations, and outperforms COSMOS even when using as few as 1-direction data. This is made possible by a nonlinear forward-model that uses the magnitude as an effective prior, for which we derived a simple gradient descent update rule. We synergistically combine this physics-model with a Variational Network (VN) to leverage the power of deep learning in the VaNDI algorithm. This technique adopts the simple gradient descent rule from NDI and learns the network parameters during training, hence requires no additional parameter tuning. Further, we evaluate NDI at 7T using highly accelerated Wave-CAIPI acquisitions at 0.5 mm isotropic resolution and demonstrate high-quality QSM from as few as 2-direction data.

Patient-specific abdominal aortic aneurysms (AAAs) are characterized by local curvature changes, which we assess using a feature-based approach on topologies representative of the AAA outer wall surface. The application of image segmentation methods yields 3D reconstructed surface polygons that contain low-quality elements, unrealistic sharp corners, and surface irregularities. To optimize the quality of the surface topology, an iterative algorithm was developed to perform interpolation of the AAA geometry, topology refinement, and smoothing. Triangular surface topologies are generated based on a Delaunay triangulation algorithm, which is adapted for AAA segmented masks. The boundary of the AAA wall is represented using a signed distance function prior to triangulation. The irregularities on the surface are minimized by an interpolation scheme and the initial coarse triangulation is refined by forcing nodes into equilibrium positions. A surface smoothing algorithm based on a low-pass filter is applied to remove sharp corners. The optimal number of iterations needed for polygon refinement and smoothing is determined by imposing a minimum average element quality index with no significant AAA sac volume change. This framework automatically generates high-quality triangular surface topologies that can be used to characterize local curvature changes of the AAA wall.

Diffusion Spectrum Imaging (DSI) reveals detailed local diffusion properties at the expense of substantially long imaging times. It is possible to accelerate acquisition by undersampling in q-space, followed by image reconstruction that exploits prior knowledge on the diffusion probability density functions (pdfs). Previously proposed methods impose this prior in the form of sparsity under wavelet and total variation (TV) transforms, or under adaptive dictionaries that are trained on example datasets to maximize the sparsity of the representation. These compressed sensing (CS) methods require full-brain processing times on the order of hours using Matlab running on a workstation. This work presents two dictionary-based reconstruction techniques that use analytical solutions, and are two orders of magnitude faster than the previously proposed dictionary-based CS approach. The first method generates a dictionary from the training data using Principal Component Analysis (PCA), and performs the reconstruction in the PCA space. The second proposed method applies reconstruction using pseudoinverse with Tikhonov regularization with respect to a dictionary. This dictionary can either be obtained using the K-SVD algorithm, or it can simply be the training dataset of pdfs without any training. All of the proposed methods achieve reconstruction times on the order of seconds per imaging slice, and have reconstruction quality comparable to that of dictionary-based CS algorithm.

With the same scan time, random SENSE+TV yields lower RMSEs of metabolite maps than other methods evaluated. Random SENSE+TV achieves up to 4.5-fold acceleration with comparable data quality as the fully sampled acquisition. Magn Reson Med 74:13-24, 2015. © 2014 Wiley Periodicals, Inc.