Dynamic MRI of the abdomen using parallel non-Cartesian convolutional recurrent neural networks

PURPOSE

To improve the image quality and reduce computational time for the reconstruction of undersampled non-Cartesian abdominal dynamic parallel MR data using the deep learning approach.

METHODS

An algorithm of parallel non-Cartesian convolutional recurrent neural networks (PNCRNNs) was developed to enable the use of the redundant information in both spatial and temporal domains, and achieve data fidelity for the reconstruction of non-Cartesian parallel MR data. The performance of PNCRNNs was evaluated for various acceleration rates, motion patterns, and imaging applications in comparison with that of the state-of-the-art algorithms of dynamic imaging, including extra-dimensional golden-angle radial sparse parallel MRI (XD-GRASP), low-rank plus sparse matrix decomposition (L+S), blind compressive sensing (BCS), and 3D convolutional neural networks (3D CNNs).

RESULTS

PNCRNNs increased the peak SNR of 9.07 dB compared with XD-GRASP, 9.26 dB compared with L+S, 3.48 dB compared with BCS, and 3.14 dB compared with 3D CNN at R = 16. The reconstruction time was 18 ms for each bin, which was two orders faster than that of XD-GRASP, L+S, and BCS. PNCRNNs provided good reconstruction for various motion patterns, k-space trajectories, and imaging applications.

CONCLUSION

The proposed PNCRNN provides substantial improvement of the image quality for dynamic golden-angle radial imaging of the abdomen in comparison with XD-GRASP, L+S, BCS, and 3D CNN. The reconstruction time of PNCRNN can be as fast as 50 bins per second, due to the use of the highly computational efficient Toeplitz approach.

Decomposition of the Gini index by income source for aggregated data and its applications

The Gini index is well-known for a single measure of inequality. The purpose of this article is to explore a matrix structure of the Gini index in a setting of multiple source income. Using matrices, we analyze the decomposition of the Gini index by income source and derive an explicit formula for the factors in terms of the associated percentile levels based on aggregated data reporting. Each factor is shown to be the sums of the two split off parts of the income within a percentile bracket. Both have unequalizing and equalizing contribution to the total inequality, respectively. We use R code and apply the methodology to several data sets including a sample of European aggregated income reporting in 2014 for illustration. A byproduct from the Gini decomposition provides a matrix approach to the decomposition of the associated Lorenz curve in terms of the density distribution matrix and a Toeplitz matrix.

Noise Suppression for Direction of Arrival Estimation in Co-located MIMO Sonar

Noise suppression capacity in multiple-input multiple-output (MIMO) sonar signal processing is derived under the assumption of white Gaussian noise. However, underwater noise mainly includes white Gaussian noise and colored noise. There exists a certain correlation between the noise signals received by each MIMO sonar array element. The performance of traditional direction-of-arrival (DOA) estimation methods decreases obviously in complex marine noise. In this paper, we propose a marine environment noise suppression method for MIMO applied to multiple targets’ DOA estimation. The noise field can be decomposed into a symmetric noise component and an asymmetric noise component. We use the covariance matrix imaginary component to pre-estimate the signal sources, then use the dimension reduction transformation to reconstruct the real component of the covariance matrix. The Toeplitz technique is utilized to reduce the correlation of the reconstructed covariance matrix. Thus, the subspace decomposition-based techniques such as multiple signal classification (MUSIC) can be used for multiple targets’ DOA estimation. To reduce the computational complexity of the methods, search-free direction-finding techniques such as the estimation of signal parameters via rotational invariance techniques (ESPRIT) can be utilized. As a result, the proposed methods can achieve better direction-finding performance in the condition of limited snapshots with lower computational cost. The corresponding Cramer-Rao bound (CRB) is deduced and the signal-to-noise ratio (SNR) gain obtained by dimension reduction processing is discussed. Simulation results also show the superiority of the proposed method over the existing methods.

Rapid compressed sensing reconstruction of 3D non-Cartesian MRI

PURPOSE

Conventional non-Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time-consuming reconstructions have slowed the adoption of undersampled 3D non-Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy.

METHODS

The reconstruction problem can be reformatted to exploit the Toeplitz structure of matrices that are evaluated every iteration, but it requires larger oversampling than what is strictly required by nonuniform Fourier transforms. Accordingly, we investigate relative speeds of the two approaches for various nonuniform Fourier transform kernel sizes and oversampling for both GPU and CPU implementations. Second, we introduce a method to minimize matrix sizes by estimating the image support. Finally, density compensation weights have been used as a preconditioning matrix to improve convergence, but this increases noise. We propose a more general approach to preconditioning that allows a trade-off between accuracy and convergence speed.

RESULTS

When using a GPU, the Toeplitz approach was faster for all practical parameters. Second, it was found that properly accounting for image support can prevent aliasing errors with minimal impact on reconstruction time. Third, the proposed preconditioning scheme improved convergence rates by an order of magnitude with negligible impact on noise.

CONCLUSION

With the proposed methods, 3D non-Cartesian compressed sensing with clinically relevant reconstruction times (<2 min) is feasible using practical computer resources. Magn Reson Med 79:2685-2692, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

NOVEL STRUCTURED LOW-RANK ALGORITHM TO RECOVER SPATIALLY SMOOTH EXPONENTIAL IMAGE TIME SERIES

We propose a structured low rank matrix completion algorithm to recover a time series of images consisting of linear combination of exponential parameters at every pixel, from undersampled Fourier measurements. The spatial smoothness of these parameters is exploited along with the exponential structure of the time series at every pixel, to derive an annihilation relation in the k - t domain. This annihilation relation translates into a structured low rank matrix formed from the k-t samples. We demonstrate the algorithm in the parameter mapping setting and show significant improvement over state of the art methods.

More IMPATIENT: A Gridding-Accelerated Toeplitz-based Strategy for Non-Cartesian High-Resolution 3D MRI on GPUs

Several recent methods have been proposed to obtain significant speed-ups in MRI image reconstruction by leveraging the computational power of GPUs. Previously, we implemented a GPU-based image reconstruction technique called the Illinois Massively Parallel Acquisition Toolkit for Image reconstruction with ENhanced Throughput in MRI (IMPATIENT MRI) for reconstructing data collected along arbitrary 3D trajectories. In this paper, we improve IMPATIENT by removing computational bottlenecks by using a gridding approach to accelerate the computation of various data structures needed by the previous routine. Further, we enhance the routine with capabilities for off-resonance correction and multi-sensor parallel imaging reconstruction. Through implementation of optimized gridding into our iterative reconstruction scheme, speed-ups of more than a factor of 200 are provided in the improved GPU implementation compared to the previous accelerated GPU code.