Signal and Noise in Diffusion Magnetic Resonance Images

This report summarizes the work I did within the Odyssée research group, in INRIA Sophia-Antipolis, under the supervision of Rachid Deriche. We have been working on problems related to noise in medical images, more specifically in diffusion weighted MRI, originating from physical process we are able to model. In the light of these models, the purpose of our work was to evaluate existing reconstruction methods, and to propose some refinement

Adaptive Design of Sampling Directions in Diffusion Tensor MRI and Validation on Human Brain Images

International audienceDiffusion tensor reconstruction is made possible through the acquisition of several diffusion weighted images, each corresponding to a given sampling direction in the Q-space. In this study, we address the question of sampling efficiency, and show that in case we have some prior knowledge on the diffusion characteristics, we may be able to adapt the sampling directions for better reconstruction of the diffusion tensor. The prior is a tensor distribution function, estimated over a given region of interest, possibly on several subjects. We formulate an energy related to error on tensor reconstruction, and calculate analytical gradient expression for efficient minimization. We validate our approach on a set of 5199 tensors taken within the corpus callosum of the human brain, and show improvement by an order of 10% on the MSE of the reconstructed tensor

A Computational Framework for Experimental Design in Diffusion MRI

International audienceIn this work, we develop a computational framework for optimal design of experiment in parametric signal reconstruction. We apply this to the optimal design of one dimensional Q-space, Q-ball imaging and multiple Q-shell experimental design. We present how to construct sampling scheme leading to minimal condition number, and compare to state-of-the-art sampling methods. We show in particular a better noise performance of these scheme through Monte-Carlo simulations for the reconstruction of synthetic signal. This demonstrates the impact of this computational framework on acquisition in diffusion MRI

Diffusion MRI Signal Reconstruction with Continuity Constraint and Optimal Regularization

International audienceIn diffusion MRI, the reconstruction of the full Ensemble Average Propagator (EAP) provides new insights in the diffusion process and the underlying microstructure. The reconstruction of the signal in the whole Q-space is still extremely challenging however. It requires very long acquisition protocols, and robust reconstruction to cope with the very low SNR at large b-values. Several reconstruction methods were proposed recently, among which the Spherical Polar Fourier (SPF) expansion, a promising basis for signal reconstruction. Yet the reconstruction in SPF is still subject to noise and discontinuity of the reconstruction. In this work, we present a method for the reconstruction of the diffusion attenuation in the whole Q-space, with a special focus on continuity and optimal regularization. We derive a modified Spherical Polar Fourier (mSPF) basis, orthonormal and compatible with SPF, for the reconstruction of a signal with continuity constraint. We also derive the expression of a Laplace regularization operator in the basis, together with a method based on generalized cross validation for the optimal choice of the parameter. Our method results in a noticeable dimension reduction as compared with SPF. Tested on synthetic and real data, the reconstruction with this method is more robust to noise and better preserves fiber directions and crossings

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

International audienceWe 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

Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging

International audienceIn diffusion MRI (dMRI) domain, many High Angular Resolution Diffusion Imaging (HARDI) methods were proposed to estimate Ensemble Average Propagator (EAP) and Orientation Distribution Function (ODF). They normally need many samples, which limits their applications. Some Compressive Sensing (CS) based methods were proposed to estimate ODF in Q-Ball Imaging (QBI) from limited samples. However EAP estimation is much more difficult than ODF in QBI. Recently Spherical Polar Fourier Imaging (SPFI) was proposed to represent diffusion signal using Spherical Polar Fourier (SPF) basis without specific assumption on diffusion signals and analytically obtain EAP and ODF via the Fourier dual SPF (dSPF) basis from arbitrarily sampled signal. Normally the coefficients of SPF basis are estimated via Least Square with weighted L2 norm regularization (L2-SPFI). However, L2-SPFI needs a truncated basis to avoid overfitting, which brings some estimation errors. By considering the Fourier relationship between EAP and signal and the Fourier basis pair provided in SPFI, we propose a novel EAP estimation method, named L1-SPFI, to estimate EAP from limited samples using CS technique, and favorably compare it to the classical L2-SPFI method. L1-SPFI estimates the coefficients in SPFI using least square with weighted L1 norm regularization. The weights are designed to enhance the sparsity. L1-SPFI significantly accelerates the ordinary CS based Fourier reconstruction method. This is performed by using SPF basis pair in CS estimation process which avoids the numerical Fourier transform in each iteration step. By considering high order basis in L1 optimization, L1-SPFI improves EAP reconstruction especially for the angular resolution. The proposed L1-SPFI was validated by synthetic, phantom and real data. The CS EAP and ODF estimations are discussed in detail and we show that recovering the angular information from CS EAP requires much less samples than exact CS EAP reconstruction. Various experiments on synthetic, phantom and real data validate the fact that SPF basis can sparsely represent DW-MRI signals and L1-SPFI largely improves the CS EAP reconstruction especially the angular resolution

Design of multishell sampling schemes with uniform coverage in diffusion MRI

International audiencePURPOSE: In diffusion MRI, a technique known as diffusion spectrum imaging reconstructs the propagator with a discrete Fourier transform, from a Cartesian sampling of the diffusion signal. Alternatively, it is possible to directly reconstruct the orientation distribution function in q-ball imaging, providing so-called high angular resolution diffusion imaging. In between these two techniques, acquisitions on several spheres in q-space offer an interesting trade-off between the angular resolution and the radial information gathered in diffusion MRI. A careful design is central in the success of multishell acquisition and reconstruction techniques. METHODS: The design of acquisition in multishell is still an open and active field of research, however. In this work, we provide a general method to design multishell acquisition with uniform angular coverage. This method is based on a generalization of electrostatic repulsion to multishell. RESULTS: We evaluate the impact of our method using simulations, on the angular resolution in one and two bundles of fiber configurations. Compared to more commonly used radial sampling, we show that our method improves the angular resolution, as well as fiber crossing discrimination. DISCUSSION: We propose a novel method to design sampling schemes with optimal angular coverage and show the positive impact on angular resolution in diffusion MRI

Parametric Dictionary Learning in Diffusion MRI

International audienceIn this work, we propose an approach to exploit the ability of compressive sensing to recover diffusion MRI signal and its characteristics from a limited number of samples. Our approach is threefold. First, we learn and design a parametric dictionary from a set of training diffusion data. This provides a highly sparse representation of the diffusion signal. The use of a parametric method presents several advantages: we design a continuous representation of the signal, from which we can analytically recover some features such as the ODF; besides, the dictionary we train is acquisition-independant. Next, we use this sparse representation to reconstruct the signal of interest, using cross-validation to assess the optimal regularization parameter for each signal reconstruction. The use of cross-validation is critical in the L1 minimization problem, as the choice of the parameter is sensitive to the noise level, the number of samples, and the data sparsity. Third, we use a polynomial approach to accurately extract ODF maxima. In the last section, we motivate and describe the choice of experimental parameters for the HARDI contest

Incremental gradient table for multiple Q-shells diffusion MRI

International audienceMost studies on sampling optimality for diffusion MRI deal with single Q-shell acquisition. For single Q-shell acquisition, incremental gradient table has proved useful in clinical setup, where the subject is likely to move, or for online reconstruction. In this article, we propose a generalization of the electrostatic repulsion to generate gradient tables for multiple Q-shells acquisitions, designed for incremental reconstruction or processing of data prematurely aborted

How should tractography go forward? A Tractometer evaluation of local reconstruction and tracking

This abstract presents the Tractometer evaluation system (www.tractometer.org) and how it was used to evaluate the entries of the ISBI 2013 HARDI Reconstruction Challenge to find the best local reconstruction methods of the contest. This abstract raises questions that researchers should take into consideration when choosing and developing new dMRI methods aimed at improving tractography