Compressed Sensing based Diffusion Spectrum Imaging

Introduction: Several methods are currently used to resolve multiple fibers within a voxel including Q-space imaging such as DSI and QBI. These approaches are generally limited by the burden of dense sampling in Q-space to avoid aliasing, which makes their application to clinical studies difficult. However, compressed sensing (CS) can attain almost perfect reconstruction from incomplete random Fourier samples of the PDF if they satisfy sparsity and incoherence conditions. The sparsity condition is met if the PDF can be expanded in an orthogonal basis set using few coefficients. The incoherency condition indicates that the reconstruction basis and the sensing basis (which is the Fourier kernel in this case) should be as different as possible to reduce the number of Fourier samples [1]. The objective of this work was to investigate a novel Q-space imaging method, which we call compressed sensing diffusion spectrum imaging (CS-DSI) that applies the CS approach to the reconstruction of the probability density function (PDF) from which the orientation distribution function (ODF) is calculated. Method: This method extends the idea of CS on 2D image-k-space domain [2] to 3D Q-space-PDF domain where the measured diffusion MR signal E(q) is related to