Joint spatial-angular sparse coding for dMRI with separable dictionaries

CSR-PERT: Joint framework for MRI and HARDI data reconstruction using perturbed radial trajectory estimated from compressively sensed measurements

Radial sampling pattern is an important signal acquisition strategy in magnetic resonance imaging (MRI) owing to better immunity to motion-induced artifacts and less pronounced aliasing due to undersampling compared to the Cartesian sampling. These advantages of radial sampling can be exploited in acquisition of multidimensional signals such as High Angular Resolution Diffusion Imaging (HARDI), with tremendous scope of acceleration. Despite such benefits, gradient delays lead to samples being acquired from unknown miscentered radial trajectories, severely degrading the image reconstruction quality. In the present work, we propose Csr-Pert that is a joint framework, wherein these perturbed radial trajectories are estimated and utilized for image reconstruction from the compressively sensed measurements of (i) MRI data and (ii) HARDI data. The proposed Csr-Pert method is tested on one real MRI dataset with trajectory deviations and is observed to perform better than the existing state-of-the-art method at high acceleration factors up to 8. To the best of our knowledge, this is the first work to address the problem of estimating perturbed trajectories using the compressively sensed MRI and HARDI data. The method is also tested for varying combinations of trajectory deviations and sampling proportions. It is observed to yield very good quality HARDI reconstruction for a wide variety of scenarios. We have also demonstrated the robustness of the proposed method on real datasets in clinical settings assuming perturbed as well as noisy trajectories.

TL-HARDI: Transform learning based accelerated reconstruction of HARDI data

Diffusion magnetic resonance imaging (dMRI) is being extensively used to study the neural architecture of the brain. High angular resolution diffusion imaging (HARDI), a variant of diffusion MRI, measures the diffusion of water molecules along the angular gradient directions in the q-space. It provides better estimates of fiber orientations compared to the traditionally used diffusion tensor imaging (DTI). However, HARDI requires acquisition of relatively large number of samples leading to longer scanning times. Several approaches based on compressive sensing (CS) have been proposed to accelerate HARDI acquisition, leveraging on the sparse representation of the HARDI signal in a pre-specified sparsifying basis. In this paper, we propose to carry out reconstruction of compressively sensed HARDI data using an adaptively learned transform. The transform is learned (i) from the compressive measurements on-the-fly, thereby, eliminating the overhead of choosing fixed sparsifying transforms, and (ii) on overlapping patches of the data, thereby, capturing local image structure effectively. Experiments are conducted on multiple real HARDI data for varying sampling ratios and sampling schemes. The performance of the proposed "TL-HARDI" method is compared with the state-of-the-art methods on various known image quality metrics as well as on dMRI feature maps derived from the reconstructed images. The proposed method is observed to yield better reconstruction than the existing state-of-the-art methods in both quantitative and qualitative comparisons.

Harmonization of diffusion MRI data sets with adaptive dictionary learning

Diffusion magnetic resonance imaging can indirectly infer the microstructure of tissues and provide metrics subject to normal variability in a population. Potentially abnormal values may yield essential information to support analysis of controls and patients cohorts, but subtle confounds could be mistaken for purely biologically driven variations amongst subjects. In this work, we propose a new harmonization algorithm based on adaptive dictionary learning to mitigate the unwanted variability caused by different scanner hardware while preserving the natural biological variability of the data. Our harmonization algorithm does not require paired training data sets, nor spatial registration or matching spatial resolution. Overcomplete dictionaries are learned iteratively from all data sets at the same time with an adaptive regularization criterion, removing variability attributable to the scanners in the process. The obtained mapping is applied directly in the native space of each subject toward a scanner-space. The method is evaluated with a public database which consists of two different protocols acquired on three different scanners. Results show that the effect size of the four studied diffusion metrics is preserved while removing variability attributable to the scanner. Experiments with alterations using a free water compartment, which is not simulated in the training data, shows that the modifications applied to the diffusion weighted images are preserved in the diffusion metrics after harmonization, while still reducing global variability at the same time. The algorithm could help multicenter studies pooling their data by removing scanner specific confounds, and increase statistical power in the process.

An improved deep network for tissue microstructure estimation with uncertainty quantification

Deep learning based methods have improved the estimation of tissue microstructure from diffusion magnetic resonance imaging (dMRI) scans acquired with a reduced number of diffusion gradients. These methods learn the mapping from diffusion signals in a voxel or patch to tissue microstructure measures. In particular, it is beneficial to exploit the sparsity of diffusion signals jointly in the spatial and angular domains, and the deep network can be designed by unfolding iterative processes that adaptively incorporate historical information for sparse reconstruction. However, the number of network parameters is huge in such a network design, which could increase the difficulty of network training and limit the estimation performance. In addition, existing deep learning based approaches to tissue microstructure estimation do not provide the important information about the uncertainty of estimates. In this work, we continue the exploration of tissue microstructure estimation using a deep network and seek to address these limitations. First, we explore the sparse representation of diffusion signals with a separable spatial-angular dictionary and design an improved deep network for tissue microstructure estimation. The procedure for updating the sparse code associated with the separable dictionary is derived and unfolded to construct the deep network. Second, with the formulation of sparse representation of diffusion signals, we propose to quantify the uncertainty of network outputs with a residual bootstrap strategy. Specifically, because of the sparsity constraint in the signal representation, we perform a Lasso bootstrap strategy for uncertainty quantification. Experiments were performed on brain dMRI scans with a reduced number of diffusion gradients, where the proposed method was applied to two representative biophysical models for describing tissue microstructure and compared with state-of-the-art methods of tissue microstructure estimation. The results show that our approach compares favorably with the competing methods in terms of estimation accuracy. In addition, the uncertainty measures provided by our method correlate with estimation errors and produce reasonable confidence intervals; these results suggest potential application of the proposed uncertainty quantification method in brain studies.

Mitigating gyral bias in cortical tractography via asymmetric fiber orientation distributions

Diffusion tractography in brain connectomics often involves tracing axonal trajectories across gray-white matter boundaries in gyral blades of complex cortical convolutions. To date, gyral bias is observed in most tractography algorithms with streamlines predominantly terminating at gyral crowns instead of sulcal banks. This work demonstrates that asymmetric fiber orientation distribution functions (AFODFs), computed via a multi-tissue global estimation framework, can mitigate the effects of gyral bias, enabling fiber streamlines at gyral blades to make sharper turns into the cortical gray matter. We use ex-vivo data of an adult rhesus macaque and in-vivo data from the Human Connectome Project (HCP) to show that the fiber streamlines given by AFODFs bend more naturally into the cortex than the conventional symmetric FODFs in typical gyral blades. We demonstrate that AFODF tractography improves cortico-cortical connectivity and provides highly consistent outcomes between two different field strengths (3T and 7T).

A deep network for tissue microstructure estimation using modified LSTM units

Diffusion magnetic resonance imaging (dMRI) offers a unique tool for noninvasively assessing tissue microstructure. However, accurate estimation of tissue microstructure described by complicated signal models can be challenging when a reduced number of diffusion gradients are used. Deep learning based microstructure estimation has recently been developed and achieved promising results. In particular, optimization-based learning, where deep network structures are constructed by unfolding the iterative processes performed for solving optimization problems, has demonstrated great potential in accurate microstructure estimation with a reduced number of diffusion gradients. In this work, using the optimization-based learning strategy, we propose a deep network structure that is motivated by the use of historical information in iterative optimization for tissue microstructure estimation, and such incorporation of historical information has not been previously explored in the design of deep networks for microstructure estimation. We assume that (1) diffusion signals can be sparsely represented by a dictionary and its coefficients jointly in the spatial and angular domain, and (2) tissue microstructure can be computed from the sparse representation. Following these assumptions, our network comprises two cascaded stages. The first stage takes image patches as input and computes the spatial-angular sparse representation of the input with learned weights. Specifically, the network structure in the first stage is constructed by unfolding an iterative process for solving sparse reconstruction problems, where historical information is incorporated. The components in this network can be shown to correspond to modified long short-term memory (LSTM) units. In the second stage, fully connected layers are added to compute the mapping from the sparse representation to tissue microstructure. The weights in the two stages are learned jointly by minimizing the mean squared error of microstructure estimation. Experiments were performed on dMRI scans with a reduced number of diffusion gradients. For demonstration, we evaluated the estimation of tissue microstructure described by three signal models: the neurite orientation dispersion and density imaging (NODDI) model, the spherical mean technique (SMT) model, and the ensemble average propagator (EAP) model. The results indicate that the proposed approach outperforms competing methods.