Tensorial Spherical Polar Fourier Diffusion MRI with Optimal Dictionary Learning

  • Jian ChengEmail author
  • Dinggang Shen
  • Pew-Thian Yap
  • Peter J. Basser
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9349)


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-Squared-Error (RMSE) than both the original SPF basis and the DL-SPF dictionary.


Fractional Anisotropy Diffusion Tensor Image Sparse Representation Compressed Sensing Mean Diffusivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jian Cheng
    • 1
    Email author
  • Dinggang Shen
    • 2
  • Pew-Thian Yap
    • 2
  • Peter J. Basser
    • 1
  1. 1.Section on Tissue Biophysics and Biomimetics (STBB), PPITS, NICHD, NIBIBBethesdaUSA
  2. 2.Department of Radiology and BRICUniversity of North Carolina at Chapel HillChapel HillUSA

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