This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal operator derived from the linear operator. The preconditioner does not assume any explicit structure on the linear function and thus can be deployed in diverse applications of interest. The efficacy of the preconditioner is validated on three different Magnetic Resonance Imaging applications, where it is seen to achieve faster iterative convergence while achieving similar reconstruction quality.

Purpose: To develop a respiratory-resolved motion-compensation method for free-breathing, high-resolution coronary magnetic resonance angiography using a 3D cones trajectory. Methods: To achieve respiratory-resolved 0.98 mm resolution images in a clinically relevant scan time, we undersample the imaging data with a variable-density 3D cones trajectory. For retrospective motion compensation, translational estimates from 3D image-based navigators (3D iNAVs) are used to bin the imaging data into four phases from end-expiration to end-inspiration. To ensure pseudo-random undersampling within each respiratory phase, we devise a phyllotaxis readout ordering scheme mindful of eddy current artifacts in steady state free precession imaging. Following binning, residual 3D translational motion within each phase is computed using the 3D iNAVs and corrected for in the imaging data. The noise-like aliasing characteristic of the combined phyllotaxis and cones sampling pattern is leveraged in a compressed sensing reconstruction with spatial and temporal regularization to reduce aliasing in each of the respiratory phases. Results: In a volunteer and 5 patients, respiratory motion compensation using the proposed method yields improved image quality compared to non-respiratory-resolved approaches with no motion correction and with 3D translational correction. Qualitative assessment by two cardiologists indicates the superior sharpness of coronary segments reconstructed with the proposed method (P < 0.01). Conclusion: The proposed method better mitigates motion artifacts in free-breathing, high-resolution coronary angiography exams compared to translational correction.

PURPOSE:Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for three-dimensional (3D) non-Cartesian acquisitions. One common approach is to reduce the number of coil channels actively used during reconstruction as in coil compression. While effective for Cartesian imaging, coil compression inherently loses signal energy, producing shading artifacts that compromise image quality for 3D non-Cartesian imaging. We propose coil sketching, a general and versatile method for computationally-efficient iterative MR image reconstruction. THEORY AND METHODS:We based our method on randomized sketching algorithms, a type of large-scale optimization algorithms well established in the fields of machine learning and big data analysis. We adapt the sketching theory to the MRI reconstruction problem via a structured sketching matrix that, similar to coil compression, considers high-energy virtual coils obtained from principal component analysis. But, unlike coil compression, it also considers random linear combinations of the remaining low-energy coils, effectively leveraging information from all coils. RESULTS:First, we performed ablation experiments to validate the sketching matrix design on both Cartesian and non-Cartesian datasets. The resulting design yielded both improved computatioanal efficiency and preserved signal-to-noise ratio (SNR) as measured by the inverse g-factor. Then, we verified the efficacy of our approach on high-dimensional non-Cartesian 3D cones datasets, where coil sketching yielded up to three-fold faster reconstructions with equivalent image quality. CONCLUSION:Coil sketching is a general and versatile reconstruction framework for computationally fast and memory-efficient reconstruction.

The Shinnar-Le-Roux (SLR) algorithm is widely used to design frequency selective pulses with large flip angles. We improve its design process to generate pulses with lower energy (by as much as 26%) and more accurate phase profiles. Concretely, the SLR algorithm consists of two steps: (1) an invertible transform between frequency selective pulses and polynomial pairs that represent Cayley-Klein (CK) parameters and (2) the design of the CK polynomial pair to match the desired magnetization profiles. Because the CK polynomial pair is bi-linearly coupled, the original algorithm sequentially solves for each polynomial instead of jointly. This results in sub-optimal pulses. Instead, we leverage a convex relaxation technique, commonly used for low rank matrix recovery, to address the bi-linearity. Our numerical experiments show that the resulting pulses are almost always globally optimal in practice. For slice excitation, the proposed algorithm results in more accurate linear phase profiles. And in general the improved pulses have lower energy than the original SLR pulses.

Purpose: Three-dimensional UTE MRI has shown the ability to provide simultaneous structural and functional lung imaging, but it is limited by respiratory motion and relatively low lung parenchyma SNR. The purpose of this paper is to improve this imaging by using a respiratory phase-resolved reconstruction approach, named motion-compensated low-rank reconstruction (MoCoLoR), which directly incorporates motion compensation into a low-rank constrained reconstruction model for highly efficient use of the acquired data. Theory and Methods: The MoCoLoR reconstruction is formulated as an optimization problem that includes a low-rank constraint using estimated motion fields to reduce the rank, optimizing over both the motion fields and reconstructed images. The proposed reconstruction along with XD and motion state-weighted motion-compensation (MostMoCo) methods were applied to 18 lung MRI scans of pediatric and young adult patients. The data sets were acquired under free-breathing and without sedation with 3D radial UTE sequences in approximately 5 min. After reconstruction, they went through ventilation analyses. Performance across reconstruction regularization and motion-state parameters were also investigated. Results: The in vivo experiments results showed that MoCoLoR made efficient use of the data, provided higher apparent SNR compared with state-of-the-art XD reconstruction and MostMoCo reconstructions, and yielded high-quality respiratory phase-resolved images for ventilation mapping. The method was effective across the range of patients scanned. Conclusion: The motion-compensated low-rank regularized reconstruction approach makes efficient use of acquired data and can improve simultaneous structural and functional lung imaging with 3D-UTE MRI. It enables the scanning of pediatric patients under free-breathing and without sedation.

—This work accelerates the convergence of iterative proximal methods used to solve linear inverse problems that arise from compressed sensing applications. This is achieved by designing a polynomial-based preconditioner that target the eigenvalue spectrum of the normal operator derived from the linear measurement matrix in a manner that does not assume any explicit structure. The resulting preconditioner can thus be deployed in diverse applications of interest. The efficacy of the preconditioner is validated on four different MRI applications, where it is seen to achieve faster convergence while achieving similar reconstruction quality.

Most deep learning (DL) magnetic resonance imaging (MRI) reconstruction approaches rely on supervised training algorithms, which require access to high-quality, fully-sampled ground truth datasets. In MRI, acquiring fully-sampled data is time-consuming, expensive, and, in some cases, impossible due to limitations on data acquisition speed. We present a DL framework for MRI reconstruction that does not require any fully-sampled data using unsupervised generative adversarial networks. We test our proposed method on 2D knee MRI data and 2D+time abdominal dynamic contrast enhanced (DCE) MRI data. In the DCE-MRI dataset, as is the case with many dynamic MRI sequences, ground truth was not possible to acquire and therefore, supervised DL reconstruction was not feasible. We show that our unsupervised method produces reconstructions which are better than compressed sensing in terms of image metrics and the recovery of anatomical structure, with faster inference time. In contrast to most deep learning reconstruction techniques, which are supervised, this method does not need any fully-sampled data. With the proposed method, accelerated imaging and accurate reconstruction can be performed in applications in cases where fully-sampled datasets are difficult to obtain or unavailable.

Convolutional neural networks (CNN) have emerged as a powerful tool for solving computational imaging reconstruction problems. However, CNNs are generally difficult-to-understand black-boxes. Accordingly, it is challenging to know when they will work and, more importantly, when they will fail. This limitation is a major barrier to their use in safety-critical applications like medical imaging: Is that blob in the reconstruction an artifact or a tumor? In this work we use Stein's unbiased risk estimate (SURE) to develop per-pixel confidence intervals, in the form of heatmaps, for compressive sensing reconstruction using the approximate message passing (AMP) framework with CNN-based denoisers. These heatmaps tell end-users how much to trust an image formed by a CNN, which could greatly improve the utility of CNNs in various computational imaging applications.

Model-based deep learning approaches, such as unrolled neural networks, have been shown to be effective tools for efficiently solving inverse problems. However, the memory costs of training unrolled networks remain high, especially when the target data is high-resolution and high-dimensional. This often requires trade-offs in either network depth to reduce model size, or data resolution to reduce data size. To address this, we propose DL-Subspace - a novel unrolled network architecture which reduces memory usage by solving for a compact, low-dimensional representation of the target instead of the target itself. DL-Subspace is applied to accelerated magnetic resonance image reconstruction, demonstrating up to 4 × higher memory efficiency and 4 × faster inference speed while maintaining similar image quality as conventional unrolled networks.

PURPOSE:ESPIRiT is a parallel imaging method that estimates coil sensitivity maps from the auto-calibration region (ACS). This requires choosing several parameters for the optimal map estimation. While fairly robust to these parameter choices, occasionally, poor selection can result in reduced performance. The purpose of this work is to automatically select parameters in ESPIRiT for more robust and consistent performance across a variety of exams. METHODS:By viewing ESPIRiT as a denoiser, Stein's unbiased risk estimate (SURE) is leveraged to automatically optimize parameter selection in a data-driven manner. The optimum parameters corresponding to the minimum true squared error, minimum SURE as derived from densely sampled, high-resolution, and non-accelerated data and minimum SURE as derived from ACS are compared using simulation experiments. To avoid optimizing the rank of ESPIRiT's auto-calibrating matrix (one of the parameters), a heuristic derived from SURE-based singular value thresholding is also proposed. RESULTS:Simulations show SURE derived from the densely sampled, high-resolution, and non-accelerated data to be an accurate estimator of the true mean squared error, enabling automatic parameter selection. The parameters that minimize SURE as derived from ACS correspond well to the optimal parameters. The soft-threshold heuristic improves computational efficiency while providing similar results to an exhaustive search. In-vivo experiments verify the reliability of this method. CONCLUSIONS:Using SURE to determine ESPIRiT parameters allows for automatic parameter selections. In-vivo results are consistent with simulation and theoretical results.

Deep learning-based image reconstruction methods have achieved promising results across multiple MRI applications. However, most approaches require large-scale fully-sampled ground truth data for supervised training. Acquiring fully-sampled data is often either difficult or impossible, particularly for dynamic contrast enhancement (DCE), 3D cardiac cine, and 4D flow. We present a deep learning framework for MRI reconstruction without any fully-sampled data using generative adversarial networks. We test the proposed method in two scenarios: retrospectively undersampled fast spin echo knee exams and prospectively undersampled abdominal DCE. The method recovers more anatomical structure compared to conventional methods.

Dynamic contrast-enhanced magnetic resonance imaging (DCE- MRI) is a widely used multi-phase technique routinely used in clinical practice. DCE and similar datasets of dynamic medical data tend to contain redundant information on the spatial and temporal components that may not be relevant for detection of the object of interest and result in unnecessarily complex computer models with long training times that may also under-perform at test time due to the abundance of noisy heterogeneous data. This work attempts to increase the training efficacy and performance of deep networks by determining redundant information in the spatial and spectral components and show that the performance of segmentation accuracy can be maintained and potentially improved. Reported experiments include the evaluation of training/testing efficacy on a heterogeneous dataset composed of abdominal images of pediatric DCE patients, showing that drastic data reduction (higher than 80%) can preserve the dynamic information and performance of the segmentation model, while effectively suppressing noise and unwanted portion of the images.

This repository contains the raw data for the second lung MRI result in Extreme MRI: Large-Scale Volumetric Dynamic Imaging from Continuous Non-Gated Acquisitions. The data is stored as numpy arrays, containing k-space data (ksp.npy), coordinates (coord.npy), and density compensation factors (dcf.npy). Code to process and reconstruct the data is available here: https://github.com/mikgroup/extreme_mri For more information about how the data is acquired, please see the linked paper.

PurposeTo rapidly reconstruct undersampled 3D non‐Cartesian image‐based navigators (iNAVs) using an unrolled deep learning (DL) model, enabling nonrigid motion correction in coronary magnetic resonance angiography (CMRA).MethodsAn end‐to‐end unrolled network is trained to reconstruct beat‐to‐beat 3D iNAVs acquired during a CMRA sequence. The unrolled model incorporates a nonuniform FFT operator in TensorFlow to perform the data‐consistency operation, and the regularization term is learned by a convolutional neural network (CNN) based on the proximal gradient descent algorithm. The training set includes 6,000 3D iNAVs acquired from 7 different subjects and 11 scans using a variable‐density (VD) cones trajectory. For testing, 3D iNAVs from 4 additional subjects are reconstructed using the unrolled model. To validate reconstruction accuracy, global and localized motion estimates from DL model‐based 3D iNAVs are compared with those extracted from 3D iNAVs reconstructed with ‐ESPIRiT. Then, the high‐resolution coronary MRA images motion corrected with autofocusing using the ‐ESPIRiT and DL model‐based 3D iNAVs are assessed for differences.Results3D iNAVs reconstructed using the DL model‐based approach and conventional ‐ESPIRiT generate similar global and localized motion estimates and provide equivalent coronary image quality. Reconstruction with the unrolled network completes in a fraction of the time compared to CPU and GPU implementations of ‐ESPIRiT (20× and 3× speed increases, respectively).ConclusionsWe have developed a deep neural network architecture to reconstruct undersampled 3D non‐Cartesian VD cones iNAVs. Our approach decreases reconstruction time for 3D iNAVs, while preserving the accuracy of nonrigid motion information offered by them for correction.

Quantitative T2* MRI is the standard of care for the assessment of iron overload. However, patient motion corrupts T2* estimates.

Compressed sensing (CS) takes advantage of a low-dimensional signal structure to reduce sampling requirements to far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transforms, finite differences, and low-rank extensions. Though powerful, these image priors are phenomenological in nature and do not account for the mechanism behind the image formation. On the other hand, MRI signal dynamics are governed by physical laws, which can be explicitly modeled and used as priors for reconstruction. These explicit and implicit signal priors can be synergistically combined in an inverse-problem framework to recover sharp, multicontrast images from highly accelerated scans. Furthermore, the physics-based constraints provide a recipe for recovering quantitative, biophysical parameters from the data.

PURPOSE:To develop a framework to reconstruct large-scale volumetric dynamic MRI from rapid continuous and non-gated acquisitions, with applications to pulmonary and dynamic contrast-enhanced (DCE) imaging.THEORY AND METHODS:The problem considered here requires recovering 100 gigabytes of dynamic volumetric image data from a few gigabytes of k-space data, acquired continuously over several minutes. This reconstruction is vastly under-determined, heavily stressing computing resources as well as memory management and storage. To overcome these challenges, we leverage intrinsic three-dimensional (3D) trajectories, such as 3D radial and 3D cones, with ordering that incoherently cover time and k-space over the entire acquisition. We then propose two innovations: (a) A compressed representation using multiscale low-rank matrix factorization that constrains the reconstruction problem, and reduces its memory footprint. (b) Stochastic optimization to reduce computation, improve memory locality, and minimize communications between threads and processors. We demonstrate the feasibility of the proposed method on DCE imaging acquired with a golden-angle ordered 3D cones trajectory and pulmonary imaging acquired with a bit-reversed ordered 3D radial trajectory. We compare it with "soft-gated" dynamic reconstruction for DCE and respiratory-resolved reconstruction for pulmonary imaging.RESULTS:The proposed technique shows transient dynamics that are not seen in gating-based methods. When applied to datasets with irregular, or non-repetitive motions, the proposed method displays sharper image features.CONCLUSIONS:We demonstrated a method that can reconstruct massive 3D dynamic image series in the extreme undersampling and extreme computation setting.

First-order gradient methods are commonly used for compressed sensing reconstruction. However, for Fourier sampling systems, they require computing a large number of fast Fourier transforms (FFTs), which can be expensive in real-time applications. In this paper, instead of random sub-sampling, we use a sampling scheme inspired by coding theory from a recent sparse-FFT work of Pawar and Ramchandran [1]. In particular, we show that Iterative Soft Thresholding Algorithm (ISTA) applied on the Least Absolute Shrinkage and Selection Operator (LASSO) with the coded sampling provides an O(log n) per-iteration speedup over the standard iteration cost, where n is the signal length. Since the coded sampling operation deviates from the common randomized compressed sensing sampling, it is a priori unclear whether LASSO can recover sparse signals. We provide recovery guarantees for LASSO using the coded sampling guaranteed for an arbitrary signal-to-noise ratio. For a k-sparse signal and under a uniformly random sparsity model, we show that LASSO recovers the underlying signal from O(k log4 n) measurements through the coded sensing system, with a reconstruction error that is proportional to the sparsity level and noise energy. Moreover, we demonstrate numerically computational speedups for using this scheme as well as lower MRI acquisition times.

We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density compensations which sacrifice reconstruction accuracy, or circulant preconditioners which increase per-iteration computation. Our approach overcomes both shortcomings. Concretely, we show that viewing the reconstruction problem in the dual formulation allows us to precondition in k-space using density-compensation-like operations. Using the primal-dual hybrid gradient method, the proposed preconditioning method does not have inner loops and are competitive in accelerating convergence compared to existing algorithms. We derive l2 -optimized preconditioners, and demonstrate through experiments that the proposed method converges in about ten iterations in practice.

In this paper, we broadly connect kernel-based filtering (e.g., approaches such as the bilateral filter and non-local means, but also many more) with general variational formulations of Bayesian regularized least squares and the related concept of proximal operators. Variational/Bayesian/proximal formulations often result in optimization problems that do not have closed-form solutions and therefore typically require global iterative solutions. Our main contribution here is to establish how one can approximate the solution of the resulting global optimization problems using locally adaptive filters with specific kernels. Our results are valid for small regularization strength (i.e., weak noise), but the approach is powerful enough to be useful for a wide range of applications because we expose how to derive a “kernelized” solution to these problems that approximates the global solution in one shot, using only local operations. As another side benefit in the reverse direction, given a local data-adaptive filter constructed with a particular choice of kernel, we enable the interpretation of such filters in the variational/Bayesian/proximal framework.