Efficient and robust computation of PDF features from diffusion MR signal

Abstract

We present a method for the estimation of various features of the tissue micro-architecture using the diffusion magnetic resonance imaging. The considered features are designed from the displacement probability density function (PDF). The estimation is based on two steps: first the approximation of the signal by a series expansion made of Gaussian-Laguerre and Spherical Harmonics functions; followed by a projection on a finite dimensional space. Besides, we propose to tackle the problem of the robustness to Rician noise corrupting in-vivo acquisitions. Our feature estimation is expressed as a variational minimization process leading to a variational framework which is robust to noise. This approach is very flexible regarding the number of samples and enables the computation of a large set of various features of the local tissues structure. We demonstrate the effectiveness of the method with results on both synthetic phantom and real MR datasets acquired in a clinical time-frame.

DiffusionKit: A light one-stop solution for diffusion MRI data analysis

“…In SPFI method, which was first proposed by Assemlal et al (Assemlal et al, 2009), the diffusion signal attenuation can be represented by the spherical polar Fourier basis functions in Eq. 5…”

“…where, q=qu and u is the unit vector, is the scale factor, is the Gamma function, Y is the real spherical harmonic (SH) basis, and L is the generalized Laguerre polynomial (Assemlal et al, 2009;Cheng et al, 2010a;Cheng et al, 2010d). Furthermore, Cheng and his colleagues proposed an analytical solution for transforming the coefficients of E(q) to the coefficients of the diffusion ODF proposed by Wedeen et al (2005) and the coefficients of EAP profile represented by the spherical harmonics basis.…”

Apparent Intravoxel Fibre Population Dispersion (FPD) Using Spherical Harmonics

“…A reconstruction step is then used to estimate the 3D diffusion probability density function (PDF) from the acquired images [2]. Recently a Spherical Polar Fourier (SPF) expansion method has been introduced in [3], which takes full advantage of the acquisition protocol. Here the MR signal attenuation E at the diffusion wave-vector q of the q-space (a subset of Euclidean R 3 ) is expressed as the following series in the SPF basis:…”

“…Let L 2 (S 2 ) denote the space of square integrable functions on S 2 . It has been shown in [3] that any feature f ∈ L 2 (S 2 ) of the diffusion PDF can be directly extracted from the modeled diffusion signal in the SPF expansion [3] as…”

“…Other spherical features of the diffusion PDF are given in [3,4]. Given a spherical feature f ∈ L 2 (S 2 ) such as (3), which represents the orientation features of the diffusion PDF, this paper presents a method to compute the statistical dispersion of fibre populations within a voxel, without any prior assumptions on their number or shape (Section 2).…”