Comparison of sampling strategies and sparsifying transforms to improve compressed sensing diffusion spectrum imaging.

PURPOSE: Diffusion Spectrum Imaging enables to reconstruct the ensemble average propagator (EAP) at the expense of having to acquire a large number of measurements. Compressive sensing offers an efficient way to decrease the required number of measurements. The purpose of this work is to perform a thorough experimental comparison of three sampling strategies and six sparsifying transforms to show their impact when applied to accelerate compressive sensing-diffusion spectrum imaging. METHODS: We propose a novel sampling scheme that assures uniform angular and random radial q-space samples. We also compare and implement six discrete sparse representations of the EAP and thoroughly evaluate them on synthetic and real data using metrics from the full EAP, kurtosis, and orientation distribution function. RESULTS: The discrete wavelet transform with Cohen-Daubechies-Feauveau 9/7 wavelets and uniform angular sampling in combination with random radial sampling showed to be better than other tested techniques to accurately reconstruct the EAP and its features. CONCLUSION: It is important to jointly optimize the sampling scheme and the sparsifying transform to obtain accelerated compressive sensing-diffusion spectrum imaging. Experiments on synthetic and real human brain data show that one can robustly recover both radial and angular EAP features while undersampling the acquisition to 64 measurements (undersampling factor of 4).

Quantitative comparison of reconstruction methods for intra-voxel fiber recovery from diffusion MRI.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

A computational diffusion MRI and parametric dictionary learning framework for modeling the diffusion signal and its features.

In this work, we first propose an original and efficient computational framework to model continuous diffusion MRI (dMRI) signals and analytically recover important diffusion features such as the Ensemble Average Propagator (EAP) and the Orientation Distribution Function (ODF). Then, we develop an efficient parametric dictionary learning algorithm and exploit the sparse property of a well-designed dictionary to recover the diffusion signal and its features with a reduced number of measurements. The properties and potentials of the technique are demonstrated using various simulations on synthetic data and on human brain data acquired from 7T and 3T scanners. It is shown that the technique can clearly recover the dMRI signal and its features with a much better accuracy compared to state-of-the-art approaches, even with a small and reduced number of measurements. In particular, we can accurately recover the ODF in regions of multiple fiber crossing, which could open new perspectives for some dMRI applications such as fiber tractography.

Continuous diffusion signal, EAP and ODF estimation via Compressive Sensing in diffusion MRI.

In this paper, we exploit the ability of Compressed Sensing (CS) to recover the whole 3D Diffusion MRI (dMRI) signal from a limited number of samples while efficiently recovering important diffusion features such as the Ensemble Average Propagator (EAP) and the Orientation Distribution Function (ODF). Some attempts to use CS in estimating diffusion signals have been done recently. However, this was mainly an experimental insight of CS capabilities in dMRI and the CS theory has not been fully exploited. In this work, we also propose to study the impact of the sparsity, the incoherence and the RIP property on the reconstruction of diffusion signals. We show that an efficient use of the CS theory enables to drastically reduce the number of measurements commonly used in dMRI acquisitions. Only 20-30 measurements, optimally spread on several b-value shells, are shown to be necessary, which is less than previous attempts to recover the diffusion signal using CS. This opens an attractive perspective to measure the diffusion signals in white matter within a reduced acquisition time and shows that CS holds great promise and opens new and exciting perspectives in diffusion MRI (dMRI).

Tractography via the ensemble average propagator in diffusion MRI.

It's well known that in diffusion MRI (dMRI), fibre crossing is an important problem for most existing diffusion tensor imaging (DTI) based tractography algorithms. To overcome these limitations, High Angular Resolution Diffusion Imaging (HARDI) based tractography has been proposed with a particular emphasis on the the Orientation Distribution Function (ODF). In this paper, we advocate the use of the Ensemble Average Propagator (EAP) instead of the ODF for tractography in dMRI and propose an original and efficient EAP-based tractography algorithm that outperforms the classical ODF-based tractography, in particular, in the regions that contain complex fibre crossing configurations. Various experimental results including synthetic, phantom and real data illustrate the potential of the approach and clearly show that our method is especially efficient to handle regions where fiber bundles are crossing, and still well handle other fiber bundle configurations such as U-shape and kissing fibers.

Parametric dictionary learning for modeling EAP and ODF in diffusion MRI.

In this work, we propose an original and efficient approach to exploit the ability of Compressed Sensing (CS) to recover diffusion MRI (dMRI) signals from a limited number of samples while efficiently recovering important diffusion features such as the ensemble average propagator (EAP) and the orientation distribution function (ODF). Some attempts to sparsely represent the diffusion signal have already been performed. However and contrarly to what has been presented in CS dMRI, in this work we propose and advocate the use of a well adapted learned dictionary and show that it leads to a sparser signal estimation as well as to an efficient reconstruction of very important diffusion features. We first propose to learn and design a sparse and parametric dictionary from a set of training diffusion data. Then, we propose a framework to analytically estimate in closed form two important diffusion features: the EAP and the ODF. Various experiments on synthetic, phantom and human brain data have been carried out and promising results with reduced number of atoms have been obtained on diffusion signal reconstruction, thus illustrating the added value of our method over state-of-the-art SHORE and SPF based approaches.

Impact of radial and angular sampling on multiple shells acquisition in diffusion MRI.

We evaluate the impact of radial and angular sampling on multiple shells (MS) acquisition in diffusion MRI. The validation of our results is based on a new and efficient method to accurately reconstruct the Ensemble Average Propagator (EAP) in term of the Spherical Polar Fourier (SPF) basis from very few diffusion weighted magnetic resonance images (DW-MRI). This approach nicely exploits the duality between SPF and a closely related basis in which one can respectively represent the EAP and the diffusion signal using the same coefficients. We efficiently combine this relation to the recent acquisition and reconstruction technique called Compressed Sensing (CS). Based on results of multi-tensors models reconstruction, we show how to construct a robust acquisition scheme for both neural fibre orientation detection and attenuation signal/EAP reconstruction.