Projection onto Epigraph Sets for Rapid Self-Tuning Compressed Sensing MRI

Automated Parameter Selection for Accelerated MRI Reconstruction via Low-Rank Modeling of Local k-Space Neighborhoods

PURPOSE

Image quality in accelerated MRI rests on careful selection of various reconstruction parameters. A common yet tedious and error-prone practice is to hand-tune each parameter to attain visually appealing reconstructions. Here, we propose a parameter tuning strategy to automate hybrid parallel imaging (PI) - compressed sensing (CS) reconstructions via low-rank modeling of local k-space neighborhoods (LORAKS) supplemented with sparsity regularization in wavelet and total variation (TV) domains.

METHODS

For low-rank regularization, we leverage a soft-thresholding operation based on singular values for matrix rank selection in LORAKS. For sparsity regularization, we employ Stein's unbiased risk estimate criterion to select the wavelet regularization parameter and local standard deviation of reconstructions to select the TV regularization parameter. Comprehensive demonstrations are presented on a numerical brain phantom and in vivo brain and knee acquisitions. Quantitative assessments are performed via PSNR, SSIM and NMSE metrics.

RESULTS

The proposed hybrid PI-CS method improves reconstruction quality compared to PI-only techniques, and it achieves on par image quality to reconstructions with brute-force optimization of reconstruction parameters. These results are prominent across several different datasets and the range of examined acceleration rates.

CONCLUSION

A data-driven parameter tuning strategy to automate hybrid PI-CS reconstructions is presented. The proposed method achieves reliable reconstructions of accelerated multi-coil MRI datasets without the need for exhaustive hand-tuning of reconstruction parameters.

Compressed sensing based dynamic MR image reconstruction by using 3D-total generalized variation and tensor decomposition: k-t TGV-TD

PURPOSE

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) is a promising technique to accelerate dynamic cardiac MR imaging (DCMRI). For DCMRI, the CS-MRI usually exploits image signal sparsity and low-rank property to reconstruct dynamic images from the undersampled k-space data. In this paper, a novel CS algorithm is investigated to improve dynamic cardiac MR image reconstruction quality under the condition of minimizing the k-space recording.

METHODS

The sparse representation of 3D cardiac magnetic resonance data is implemented by synergistically integrating 3D total generalized variation (3D-TGV) algorithm and high order singular value decomposition (HOSVD) based Tensor Decomposition, termed k-t TGV-TD method. In the proposed method, the low rank structure of the 3D dynamic cardiac MR data is performed with the HOSVD method, and the localized image sparsity is achieved by the 3D-TGV method. Moreover, the Fast Composite Splitting Algorithm (FCSA) method, combining the variable splitting with operator splitting techniques, is employed to solve the low-rank and sparse problem. Two different cardiac MR datasets (cardiac perfusion and cine MR datasets) are used to evaluate the performance of the proposed method.

RESULTS

Compared with the state-of-art methods, such as k-t SLR, 3D-TGV, HOSVD based tensor decomposition and low-rank plus sparse method, the proposed k-t TGV-TD method can offer improved reconstruction accuracy in terms of higher peak SNR (PSNR) and structural similarity index (SSIM). The proposed k-t TGV-TD method can achieve significantly better and stable reconstruction results than state-of-the-art methods in terms of both PSNR and SSIM, especially for cardiac perfusion MR dataset.

CONCLUSIONS

This work proved that the k-t TGV-TD method was an effective sparse representation way for DCMRI, which was capable of significantly improving the reconstruction accuracy with different acceleration factors.

Real‐time imaging of respiratory effects on cerebrospinal fluid flow in small diameter passageways

Purpose

Respiration‐related CSF flow through the cerebral aqueduct may be useful for elucidating physiology and pathophysiology of the glymphatic system, which has been proposed as a mechanism of brain waste clearance. Therefore, we aimed to (1) develop a real‐time (CSF) flow imaging method with high spatial and sufficient temporal resolution to capture respiratory effects, (2) validate the method in a phantom setup and numerical simulations, and (3) apply the method in vivo and quantify its repeatability and correlation with different respiratory conditions.

Methods

A golden‐angle radial flow sequence (reconstructed temporal resolution 168 ms, spatial resolution 0.6 mm) was implemented on a 7T MRI scanner and reconstructed using compressed sensing. A phantom setup mimicked simultaneous cardiac and respiratory flow oscillations. The effect of temporal resolution and vessel diameter was investigated numerically. Healthy volunteers (n = 10) were scanned at four different respiratory conditions, including repeat scans.

Results

Phantom data show that the developed sequence accurately quantifies respiratory oscillations (ratio real‐time/reference Q_R = 0.96 ± 0.02), but underestimates the rapid cardiac oscillations (ratio Q_C = 0.46 ± 0.14). Simulations suggest that Q_C can be improved by increasing temporal resolution. In vivo repeatability was moderate to very strong for cranial and caudal flow (intraclass correlation coefficient range: 0.55–0.99) and weak to strong for net flow (intraclass correlation coefficient range: 0.48–0.90). Net flow was influenced by respiratory condition (p < 0.01).

Conclusions

The presented real‐time flow MRI method can quantify respiratory‐related variations of CSF flow in the cerebral aqueduct, but it underestimates rapid cardiac oscillations. In vivo, the method showed good repeatability and a relationship between flow and respiration.

Compressed Sensing MRI with ℓ1-Wavelet Reconstruction Revisited Using Modern Data Science Tools

Deep learning (DL) has emerged as a powerful tool for improving the reconstruction quality of accelerated MRI. These methods usually show enhanced performance compared to conventional methods, such as compressed sensing (CS) and parallel imaging. However, in most scenarios, CS is implemented with two or three empirically-tuned hyperparameters, while a plethora of advanced data science tools are used in DL. In this work, we revisit ℓ1 -wavelet CS for accelerated MRI using modern data science tools. By using tools like algorithm unrolling and end-to-end training with stochastic gradient descent over large databases that DL algorithms utilize, and combining these with conventional concepts like wavelet sub-band processing and reweighted ℓ1 minimization, we show that ℓ1-wavelet CS can be fine-tuned to a level comparable to DL methods. While DL uses hundreds of thousands of parameters, the proposed optimized ℓ1-wavelet CS with sub-band training and reweighting uses only 128 parameters, and employs a fully-explainable convex reconstruction model.

Utilizing the Wavelet Transform's Structure in Compressed Sensing

Compressed sensing has empowered quality image reconstruction with fewer data samples than previously thought possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is commonly used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns using both magnetic resonance and optical images.

Two-stage deep learning for accelerated 3D time-of-flight MRA without matched training data

Time-of-flight magnetic resonance angiography (TOF-MRA) is one of the most widely used non-contrast MR imaging methods to visualize blood vessels, but due to the 3-D volume acquisition highly accelerated acquisition is necessary. Accordingly, high quality reconstruction from undersampled TOF-MRA is an important research topic for deep learning. However, most existing deep learning works require matched reference data for supervised training, which are often difficult to obtain. By extending the recent theoretical understanding of cycleGAN from the optimal transport theory, here we propose a novel two-stage unsupervised deep learning approach, which is composed of the multi-coil reconstruction network along the coronal plane followed by a multi-planar refinement network along the axial plane. Specifically, the first network is trained in the square-root of sum of squares (SSoS) domain to achieve high quality parallel image reconstruction, whereas the second refinement network is designed to efficiently learn the characteristics of highly-activated blood flow using double-headed projection discriminator. Extensive experiments demonstrate that the proposed learning process without matched reference exceeds performance of state-of-the-art compressed sensing (CS)-based method and provides comparable or even better results than supervised learning approaches.

The Role of Redundant Bases and Shrinkage Functions in Image Denoising

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image, in the transform domain, using a set of shrinkage functions (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used. For example, it is widely known that applying SFs in a redundant basis improves the results. However, it is barely known that the shape of the SFs should be changed when the transform used is redundant. In this paper, we introduce a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimized. We suggest three schemes for optimizing the SFs and provide bounds of the remaining noise, in each scheme, with respect to the other alternatives. In particular, we show that for subband optimization, where each SF is optimized independently for a particular band, optimizing the SFs in the spatial domain is always better than or equal to optimizing the SFs in the transform domain. Furthermore, for redundant bases, we provide the expected denoising gain that can be achieved, relative to the unitary basis, as a function of the redundancy rate.

Self-supervised learning of physics-guided reconstruction neural networks without fully sampled reference data

PURPOSE

To develop a strategy for training a physics-guided MRI reconstruction neural network without a database of fully sampled data sets.

METHODS

Self-supervised learning via data undersampling (SSDU) for physics-guided deep learning reconstruction partitions available measurements into two disjoint sets, one of which is used in the data consistency (DC) units in the unrolled network and the other is used to define the loss for training. The proposed training without fully sampled data is compared with fully supervised training with ground-truth data, as well as conventional compressed-sensing and parallel imaging methods using the publicly available fastMRI knee database. The same physics-guided neural network is used for both proposed SSDU and supervised training. The SSDU training is also applied to prospectively two-fold accelerated high-resolution brain data sets at different acceleration rates, and compared with parallel imaging.

RESULTS

Results on five different knee sequences at an acceleration rate of 4 shows that the proposed self-supervised approach performs closely with supervised learning, while significantly outperforming conventional compressed-sensing and parallel imaging, as characterized by quantitative metrics and a clinical reader study. The results on prospectively subsampled brain data sets, in which supervised learning cannot be used due to lack of ground-truth reference, show that the proposed self-supervised approach successfully performs reconstruction at high acceleration rates (4, 6, and 8). Image readings indicate improved visual reconstruction quality with the proposed approach compared with parallel imaging at acquisition acceleration.

CONCLUSION

The proposed SSDU approach allows training of physics-guided deep learning MRI reconstruction without fully sampled data, while achieving comparable results with supervised deep learning MRI trained on fully sampled data.