Tensorial Spherical Polar Fourier Diffusion MRI with Optimal Dictionary Learning
High Angular Resolution Diffusion Imaging (HARDI) can characterize complex white matter micro-structure, avoiding the Gaussian diffusion assumption inherent in Diffusion Tensor Imaging (DTI). However, HARDI methods normally require significantly more sign
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Section on Tissue Biophysics and Biomimetics (STBB), PPITS, NICHD, NIBIB Department of Radiology and BRIC, University of North Carolina at Chapel Hill, USA {jian.cheng,pb12q}@nih.gov
Abstract. High Angular Resolution Diffusion Imaging (HARDI) can characterize complex white matter micro-structure, avoiding the Gaussian diffusion assumption inherent in Diffusion Tensor Imaging (DTI). However, HARDI methods normally require significantly more signal measurements and a longer scan time than DTI, which limits its clinical utility. By considering sparsity of the diffusion signal, Compressed Sensing (CS) allows robust signal reconstruction from relatively fewer samples, reducing the scanning time. A good dictionary that sparsifies the signal is crucial for CS reconstruction. In this paper, we propose a novel method called Tensorial Spherical Polar Fourier Imaging (TSPFI) to recover continuous diffusion signal and diffusion propagator by representing the diffusion signal using an orthonormal TSPF basis. TSPFI is a generalization of the existing model-based method DTI and the model-free method SPFI. We also propose dictionary learning TSPFI (DL-TSPFI) to learn an even sparser dictionary represented as a linear combination of TSPF basis from continuous mixture of Gaussian signals. The learning process is efficiently performed in a small subspace of SPF coefficients, and the learned dictionary is proved to be sparse for all mixture of Gaussian signals by adaptively setting the tensor in TSPF basis. Then the learned DL-TSPF dictionary is optimally and adaptively applied to different voxels using DTI and a weighted LASSO for CS reconstruction. DL-TSPFI is a generalization of DL-SPFI, by considering general adaptive tensor setting instead of a scale value. The experiments demonstrated that the learned DL-TSPF dictionary has a sparser representation and lower reconstruction Root-Mean-SquaredError (RMSE) than both the original SPF basis and the DL-SPF dictionary.
1 Introduction Diffusion MRI (dMRI) is a unique non-invasive imaging technique to explore white matter in human brain by measuring the diffusion of water molecules. The diffusion process is fully characterized by the diffusion propagator P(R), called the Ensemble Average Propagator (EAP), in the displacement R-space [1]. With the narrow pulse assumption, the diffusion signal attenuation E(q) is the 3D Fourier transform of P(R), i.e., P(R) = R3 E(q) exp(−2πqT R)dq. A hot topic in dMRI is to recover the continuous signal E(q) and the EAP P(R) from a limited number of signal samples with noise. Diffusion Tensor Imaging (DTI) [2] is the most popular method for diffusion data reconstruction. With the Gaussian diffusion assumption, E(q) = exp(−4π2 τqT Dq) where c Springer International Publishing Switzerland 2015 N. Navab et al. (Eds.): MICCAI 2015, Part I, LNCS 9349, pp. 174–182, 2015. DOI: 10.1007/978-3-319-24553-9_22
Tensorial Spherical Polar Fourier Diffusion MRI with Optimal Dictionary Learning
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τ is the diffusion time and D is the 3 × 3 diffusion tensor. Ma
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