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

Jian Cheng (1, 2) , Sylvain Merlet (2) , Aurobrata Ghosh (2) , Emmanuel Caruyer (2) , Tianzi Jiang (1) , Rachid Deriche (2)

1 LIAMA - Brain imaging
2 ATHENA - Computational Imaging of the Central Nervous System

Since Diffusion Tensor Imaging (DTI) cannot detect the fiber crossing, many new works beyond DTI has been proposed to explore the q-space. Most works, known as single shell High Angular Resolution Imaging (sHARDI), focus on single shell sampling and reconstruct the Orientation Distribution Function (ODF). The ODF, which has no radial information at all, is just one of features of Ensemble Average Propagator (EAP). Diffusion Spectrum Imaging (DSI) is a standard method to estimate EAP via numerical Fourier Transform (FT), which needs lots of samples and is impractical for clinical study. Spherical Polar Fourier Imaging (SPFI) [1,2] was proposed to represent the signal using SPF basis, then the EAP and the ODF have analytical closed forms. So the estimation of the coefficients under SPF basis is very important. In [1,2], the coefficients are estimated based on a standard Least Square (LS) with L2 norm regularization (L2-L2). In this paper, we propose to estimate the coefficients using LS with L1 norm regularization (L2-L1), also named as Least Absolute Selection and Shrinkage Operator (LASSO). And we prove that the L2-L1 estimation of the coefficients is actually the well known Compressive Sensing (CS) method to estimate EAP, which brings lots of Mathematical tools and possibility to improve the sampling scheme in q-space.

Domaines: Imagerie médicale

Jian Cheng, Sylvain Merlet, Aurobrata Ghosh, Emmanuel Caruyer, Tianzi Jiang, et al.. Compressive Sensing Ensemble Average Propagator Estimation via L1 Spherical Polar Fourier Imaging. ISMRM, May 2011, Montréal, Canada. ⟨inria-00615437⟩