arXiv subjects

Michael Lustig

Publications and source records attributed to Michael Lustig.

30 records · Page 2Linked to original sources

arXiv2019

Accelerating Non-Cartesian MRI Reconstruction Convergence using k-space Preconditioning

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.

physics.med-ph↗

arXiv2019

Computational MRI with Physics-based Constraints: Application to Multi-contrast and Quantitative Imaging

Compressed sensing takes advantage of low-dimensional signal structure to reduce sampling requirements far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transform, 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. {1}These explicit and implicit signal priors can be synergistically combined in an inverse problem framework to recover sharp, multi-contrast images from highly accelerated scans. Furthermore, the physics-based constraints provide a recipe for recovering quantitative, bio-physical parameters from the data. This article introduces physics-based modeling constraints in MRI and shows how they can be used in conjunction with compressed sensing for image reconstruction and quantitative imaging. We describe model-based quantitative MRI, as well as its linear subspace approximation. We also discuss approaches to selecting user-controllable scan parameters given knowledge of the physical model. We present several MRI applications that take advantage of this framework for the purpose of multi-contrast imaging and quantitative mapping.

eess.IV↗

arXiv2018

ENLIVE: An Efficient Nonlinear Method for Calibrationless and Robust Parallel Imaging

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel imaging technique which simultaneously estimates coil profiles and image content in a relaxed forward model. Our method is robust against a wide class of data inconsistencies, minimizes imaging artifacts and is comparably fast combining important advantages of many conceptually different state-of-the-art parallel imaging approaches. Depending on the experimental setting, data can be undersampled well below the Nyquist limit. Here, even high acceleration factors yield excellent imaging results while being robust to noise and the occurrence of phase singularities in the image domain, as we show on different data. Moreover, our method successfully reconstructs acquisitions with insufficient field-of-view. We further compare our approach to ESPIRiT and SAKE using spin-echo and gradient echo MRI data from the human head and knee. In addition, we show its applicability to non-Cartesian imaging on radial FLASH cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be related to a low-rank formulation of blind multi-channel deconvolution, explaining why it inherently promotes low-rank solutions.

physics.med-ph↗

arXiv2018

Clinically Deployed Distributed Magnetic Resonance Imaging Reconstruction: Application to Pediatric Knee Imaging

Magnetic resonance imaging is capable of producing volumetric images without ionizing radiation. Nonetheless, long acquisitions lead to prohibitively long exams. Compressed sensing (CS) can enable faster scanning via sub-sampling with reduced artifacts. However, CS requires significantly higher reconstruction computation, limiting current clinical applications to 2D/3D or limited-resolution dynamic imaging. Here we analyze the practical limitations to T2 Shuffling, a four-dimensional CS-based acquisition, which provides sharp 3D-isotropic-resolution and multi-contrast images in a single scan. Our improvements to the pipeline on a single machine provide a 3x overall reconstruction speedup, which allowed us to add algorithmic changes improving image quality. Using four machines, we achieved additional 2.1x improvement through distributed parallelization. Our solution reduced the reconstruction time in the hospital to 90 seconds on a 4-node cluster, enabling its use clinically. To understand the implications of scaling this application, we simulated running our reconstructions with a multiple scanner setup typical in hospitals.

physics.med-ph↗

arXiv2017

General Phase Regularized Reconstruction using Phase Cycling

Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction was studied under a regularized inverse problem framework. A general phase regularized reconstruction algorithm was proposed to enable various joint reconstruction of partial Fourier imaging, water-fat imaging and flow imaging, along with parallel imaging (PI) and compressed sensing (CS). Since phase regularized reconstruction is inherently non-convex and sensitive to phase wraps in the initial solution, a reconstruction technique, named phase cycling, was proposed to render the overall algorithm invariant to phase wraps. The proposed method was applied to retrospectively under-sampled in vivo datasets and compared with state of the art reconstruction methods. Results: Phase cycling reconstructions showed reduction of artifacts compared to reconstructions with- out phase cycling and achieved similar performances as state of the art results in partial Fourier, water-fat and divergence-free regularized flow reconstruction. Joint reconstruction of partial Fourier + water-fat imaging + PI + CS, and partial Fourier + divergence-free regularized flow imaging + PI + CS were demonstrated. Conclusion: The proposed phase cycling reconstruction provides an alternative way to perform phase regularized reconstruction, without the need to perform phase unwrapping. It is robust to the choice of initial solutions and encourages the joint reconstruction of phase imaging applications.

cs.CV↗

arXiv2017

Better than Real: Complex-valued Neural Nets for MRI Fingerprinting

The task of MRI fingerprinting is to identify tissue parameters from complex-valued MRI signals. The prevalent approach is dictionary based, where a test MRI signal is compared to stored MRI signals with known tissue parameters and the most similar signals and tissue parameters retrieved. Such an approach does not scale with the number of parameters and is rather slow when the tissue parameter space is large. Our first novel contribution is to use deep learning as an efficient nonlinear inverse mapping approach. We generate synthetic (tissue, MRI) data from an MRI simulator, and use them to train a deep net to map the MRI signal to the tissue parameters directly. Our second novel contribution is to develop a complex-valued neural network with new cardioid activation functions. Our results demonstrate that complex-valued neural nets could be much more accurate than real-valued neural nets at complex-valued MRI fingerprinting.

cs.CV↗

arXiv2017

Multiple-coil k-space interpolation enhances resolution in single-shot spatiotemporal MRI

Purpose: Spatio-temporal encoding (SPEN) experiments can deliver single-scan MR images without folding complications and with robustness to chemical shift and susceptibility artifacts. It is here shown that further resolution improvements can arise by relying on multiple receivers, to interpolate the sampled data along the low-bandwidth dimension. The ensuing multiple-sensor interpolation is akin to recently introduced SPEN interleaving procedures, albeit without requiring multiple shots. Methods: By casting SPEN's spatial rasterization in k-space, it becomes evident that local k-data interpolations enabled by multiple receivers are akin to real-space interleaving of SPEN images. The practical implementation of such resolution-enhancing procedure becomes similar to those normally used in SMASH or SENSE, yet relaxing these methods' fold-over constraints. Results: Experiments validating the theoretical expectations were carried out on phantoms and human volunteers on a 3T scanner. The experiments showed the expected resolution enhancement, at no cost in the sequence's complexity. With the addition of multibanding and stimulated echo procedures, 48-slices full-brain coverage could be recorded free from distortions at sub-mm resolution, in 3 sec. Conclusion: Super-resolved SPEN with SENSE (SUSPENSE) achieves the goals of multi-shot SPEN interleaving within one single scan, delivering single-shot sub-mm in-plane resolutions in scanners equipped with suitable multiple sensors.

physics.chem-ph↗

arXiv2016

On the Empirical Effect of Gaussian Noise in Under-sampled MRI Reconstruction

In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which linear reconstructions will exhibit artifacts. Another consequence of under-sampling is lower signal to noise ratio (SNR) due to fewer acquired measurements. Even if an oracle provided the information to perfectly disambiguate the underdetermined system, the reconstructed image could still have lower image quality than a corresponding fully sampled acquisition because of the reduced measurement time. The effects of lower SNR and the underdetermined system are coupled during reconstruction, making it difficult to isolate the impact of lower SNR on image quality. To this end, we present an image quality prediction process that reconstructs fully sampled, fully determined data with noise added to simulate the loss of SNR induced by a given under-sampling pattern. The resulting prediction image empirically shows the effect of noise in under-sampled image reconstruction without any effect from an underdetermined system. We discuss how our image quality prediction process can simulate the distribution of noise for a given under-sampling pattern, including variable density sampling that produces colored noise in the measurement data. An interesting consequence of our prediction model is that we can show that recovery from underdetermined non-uniform sampling is equivalent to a weighted least squares optimization that accounts for heterogeneous noise levels across measurements. Through a series of experiments with synthetic and in vivo datasets, we demonstrate the efficacy of the image quality prediction process and show that it provides a better estimation of reconstruction image quality than the corresponding fully-sampled reference image.

cs.CV↗

arXiv2016

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components \revised{either exactly or approximately}. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information.

eess.SY↗

arXiv2016

Estimating Absolute-Phase Maps Using ESPIRiT and Virtual Conjugate Coils

Purpose: To develop an ESPIRiT-based method to estimate coil sensitivities with image phase as a building block for efficient and robust image reconstruction with phase constraints. Theory and Methods: ESPIRiT is a new framework for calibration of the coil sensitivities and reconstruction in parallel Magnetic Resonance Imaging (MRI). Applying ESPIRiT to a combined set of physical and virtual conjugate coils (VCC-ESPIRiT) implicitly exploits conjugate symmetry in k-space similar to VCC-GRAPPA. Based on this method, a new post-processing step is proposed for the explicit computation of coil sensitivities that include the absolute phase of the image. The accuracy of the computed maps is directly validated using a test based on projection onto fully sampled coil images and also indirectly in phase-constrained parallel-imaging reconstructions. Results: The proposed method can estimate accurate sensitivities which include low-resolution image phase. In case of high-frequency phase variations VCC-ESPIRiT yields an additional set of maps that indicates the existence of a high-frequency phase component. Taking this additional set of maps into account can improve the robustness of phase-constrained parallel imaging. Conclusion: The extended VCC-ESPIRiT is a useful tool for phase-constrained imaging.

cs.CV↗

arXiv2015

Imaging Renal Urea Handling in Rats at Millimeter Resolution using Hyperpolarized Magnetic Resonance Relaxometry

\textit{In vivo} spin spin relaxation time ($T_2$) heterogeneity of hyperpolarized \textsuperscript{13}C urea in the rat kidney was investigated. Selective quenching of the vascular hyperpolarized \textsuperscript{13}C signal with a macromolecular relaxation agent revealed that a long-$T_2$ component of the \textsuperscript{13}C urea signal originated from the renal extravascular space, thus allowing the vascular and renal filtrate contrast agent pools of the \textsuperscript{13}C urea to be distinguished via multi-exponential analysis. The $T_2$ response to induced diuresis and antidiuresis was performed with two imaging agents: hyperpolarized \textsuperscript{13}C urea and a control agent hyperpolarized bis-1,1-(hydroxymethyl)-1-\textsuperscript{13}C-cyclopropane-$^2\textrm{H}_8$. Large $T_2$ increases in the inner-medullar and papilla were observed with the former agent and not the latter during antidiuresis suggesting that $T_2$ relaxometry may be used to monitor the inner-medullary urea transporter (UT)-A1 and UT-A3 mediated urea concentrating process. Two high resolution imaging techniques - multiple echo time averaging and ultra-long echo time sub-2 mm$^3$ resolution 3D imaging - were developed to exploit the particularly long relaxation times observed.

physics.med-ph↗

arXiv2014

Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated with numerical examples.

physics.med-ph↗