Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.

MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods.

/pdf/accelerated-dynamic-mri-exploiting-sparsity-and-low-rank-2xbe0mkiiu.pdf

Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR

Purpose
To develop a fast and flexible free-breathing dynamic volumetric MRI technique, iterative Golden-angle RAdial Sparse Parallel MRI (iGRASP), that combines compressed sensing, parallel imaging, and golden-angle radial sampling.

Methods
Radial k-space data are acquired continuously using the golden-angle scheme and sorted into time series by grouping an arbitrary number of consecutive spokes into temporal frames. An iterative reconstruction procedure is then performed on the undersampled time series where joint multicoil sparsity is enforced by applying a total-variation constraint along the temporal dimension. Required coil-sensitivity profiles are obtained from the time-averaged data.

Results
iGRASP achieved higher acceleration capability than either parallel imaging or coil-by-coil compressed sensing alone. It enabled dynamic volumetric imaging with high spatial and temporal resolution for various clinical applications, including free-breathing dynamic contrast-enhanced imaging in the abdomen of both adult and pediatric patients, and in the breast and neck of adult patients.

Conclusion
The high performance and flexibility provided by iGRASP can improve clinical studies that require robustness to motion and simultaneous high spatial and temporal resolution. Magn Reson Med 72:707–717, 2014. © 2013 Wiley Periodicals, Inc.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mrm.24980

Golden-angle radial sparse parallel MRI: combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI

Total variation was recently introduced in many different magnetic resonance imaging applications. The assumption of total variation is that images consist of areas, which are piecewise constant. However, in many practical magnetic resonance imaging situations, this assumption is not valid due to the inhomogeneities of the exciting B1 field and the receive coils. This work introduces the new concept of total generalized variation for magnetic resonance imaging, a new mathematical framework, which is a generalization of the total variation theory and which eliminates these restrictions. Two important applications are considered in this article, image denoising and image reconstruction from undersampled radial data sets with multiple coils. Apart from simulations, experimental results from in vivo measurements are presented where total generalized variation yielded improved image quality over conventional total variation in all cases.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mrm.22595

Second order total generalized variation (TGV) for MRI

Purpose
To develop a novel framework for free-breathing MRI called XD-GRASP, which sorts dynamic data into extra motion-state dimensions using the self-navigation properties of radial imaging and reconstructs the multidimensional dataset using compressed sensing.

Methods
Radial k-space data are continuously acquired using the golden-angle sampling scheme and sorted into multiple motion-states based on respiratory and/or cardiac motion signals derived directly from the data. The resulting undersampled multidimensional dataset is reconstructed using a compressed sensing approach that exploits sparsity along the new dynamic dimensions. The performance of XD-GRASP is demonstrated for free-breathing three-dimensional (3D) abdominal imaging, two-dimensional (2D) cardiac cine imaging and 3D dynamic contrast-enhanced (DCE) MRI of the liver, comparing against reconstructions without motion sorting in both healthy volunteers and patients.

Results
XD-GRASP separates respiratory motion from cardiac motion in cardiac imaging, and respiratory motion from contrast enhancement in liver DCE-MRI, which improves image quality and reduces motion-blurring artifacts.

Conclusion
XD-GRASP represents a new use of sparsity for motion compensation and a novel way to handle motions in the context of a continuous acquisition paradigm. Instead of removing or correcting motion, extra motion-state dimensions are reconstructed, which improves image quality and also offers new physiological information of potential clinical value. Magn Reson Med 75:775–788, 2016. © 2015 Wiley Periodicals, Inc.

XD-GRASP: Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing.

For patients with impaired breath-hold capacity and/or arrhythmias, real-time cine MRI may be more clinically useful than breath-hold cine MRI. However, commercially available real-time cine MRI methods using parallel imaging typically yield relatively poor spatio-temporal resolution due to their low image acquisition speed. We sought to achieve relatively high spatial resolution (∼2.5 × 2.5 mm(2)) and temporal resolution (∼40 ms), to produce high-quality real-time cine MR images that could be applied clinically for wall motion assessment and measurement of left ventricular function. In this work, we present an eightfold accelerated real-time cardiac cine MRI pulse sequence using a combination of compressed sensing and parallel imaging (k-t SPARSE-SENSE). Compared with reference, breath-hold cine MRI, our eightfold accelerated real-time cine MRI produced significantly worse qualitative grades (1-5 scale), but its image quality and temporal fidelity scores were above 3.0 (adequate) and artifacts and noise scores were below 3.0 (moderate), suggesting that acceptable diagnostic image quality can be achieved. Additionally, both eightfold accelerated real-time cine and breath-hold cine MRI yielded comparable left ventricular function measurements, with coefficient of variation <10% for left ventricular volumes. Our proposed eightfold accelerated real-time cine MRI with k-t SPARSE-SENSE is a promising modality for rapid imaging of myocardial function.

Highly accelerated real-time cardiac cine MRI using k–t SPARSE-SENSE

Purpose
To improve myocardial perfusion MRI by reconstructing undersampled radial data with a spatiotemporal constrained reconstruction method (STCR).

Acquisition and reconstruction of undersampled radial data for myocardial perfusion magnetic resonance imaging

Dynamic contrast-enhanced (DCE) MRI is a powerful technique to probe an area of interest in the body. Here a temporally constrained reconstruction (TCR) technique that requires less k-space data over time to obtain good-quality reconstructed images is proposed. This approach can be used to improve the spatial or temporal resolution, or increase the coverage of the object of interest. The method jointly reconstructs the space-time data iteratively with a temporal constraint in order to resolve aliasing. The method was implemented and its feasibility tested on DCE myocardial perfusion data with little or no motion. The results obtained from sparse k-space data using the TCR method were compared with results obtained with a sliding-window (SW) method and from full data using the standard inverse Fourier transform (IFT) reconstruction. Acceleration factors of 5 (R = 5) were achieved without a significant loss in image quality. Mean improvements of 28 +/- 4% in the signal-to-noise ratio (SNR) and 14 +/- 4% in the contrast-to-noise ratio (CNR) were observed in the images reconstructed using the TCR method on sparse data (R = 5) compared to the standard IFT reconstructions from full data for the perfusion datasets. The method has the potential to improve dynamic myocardial perfusion imaging and also to reconstruct other sparse dynamic MR acquisitions.

/pdf/temporally-constrained-reconstruction-of-dynamic-cardiac-3ntzvaf9wo.pdf

Temporally constrained reconstruction of dynamic cardiac perfusion MRI.

Purpose

To assess the accuracy of a model-based approach for registration of myocardial dynamic contrast-enhanced (DCE)-MRI corrupted by respiratory motion.



Materials and Methods

Ten patients were scanned for myocardial perfusion on 3T or 1.5T scanners, and short- and long-axis slices were acquired. Interframe registration was done using an iterative model-based method in conjunction with a mean square difference metric. The method was tested by comparing the absolute motion before and after registration, as determined from manually registered images. Regional flow indices of myocardium calculated from the manually registered data were compared with those obtained with the model-based registration technique.



Results

The mean absolute motion of the heart for the short-axis data sets over all the time frames decreased from 5.3 ± 5.2 mm (3.3 ± 3.1 pixels) to 0.8 ± 1.3 mm (0.5 ± 0.7 pixels) in the vertical direction, and from 3.0 ± 3.7 mm (1.7 ± 2.1 pixels) to 0.9 ± 1.2 mm (0.5 ± 0.7 pixels) in the horizontal direction. A mean absolute improvement of 77% over all the data sets was observed in the estimation of the regional perfusion flow indices of the tissue as compared to those obtained from manual registration. Similar results were obtained with two-chamber-view long-axis data sets.



Conclusion

The model-based registration method for DCE cardiac data is comparable to manual registration and offers a unique registration method that reduces errors in the quantification of myocardial perfusion parameters as compared to those obtained from manual registration. J. Magn. Reson. Imaging 2006. © 2006 Wiley-Liss, Inc.

Model-based registration for dynamic cardiac perfusion MRI.

Diffusion weighted imaging (DWI) is widely used to study changes in white matter following stroke. In various studies employing diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI) modalities, it has been shown that fractional anisotropy (FA), mean diffusivity (MD), and generalized FA (GFA) can be used as measures of white matter tract integrity in stroke patients. However, these measures may be non-specific, as they do not directly delineate changes in tissue microstructure. Multi-compartment models overcome this limitation by modeling DWI data using a set of indices that are directly related to white matter microstructure. One of these models which is gaining popularity, is neurite orientation dispersion and density imaging (NODDI). This model uses conventional single or multi-shell HARDI data to describe fiber orientation dispersion as well as densities of different tissue types in the imaging voxel. In this paper, we apply for the first time the NODDI model to 4-shell HARDI stroke data. By computing NODDI indices over the entire brain in two stroke patients, and comparing tissue regions in ipsilesional and contralesional hemispheres, we demonstrate that NODDI modeling provides specific information on tissue microstructural changes. We also introduce an information theoretic analysis framework to investigate the non-local effects of stroke in the white matter. Our initial results suggest that the NODDI indices might be more specific markers of white matter reorganization following stroke than other measures previously used in studies of stroke recovery.

/pdf/assessment-of-white-matter-microstructure-in-stroke-patients-3cg8pk860q.pdf

Ganesh Adluru

Papers

Highly accelerated real-time cardiac cine MRI using k–t SPARSE-SENSE

Acquisition and reconstruction of undersampled radial data for myocardial perfusion magnetic resonance imaging

Temporally constrained reconstruction of dynamic cardiac perfusion MRI.

Model-based registration for dynamic cardiac perfusion MRI.

Assessment of white matter microstructure in stroke patients using NODDI