Boosting the Angular Resolution of Q-space Imaging Methods by Diffusion Odf Deconvolution

Introduction Several deconvolution methods have been proposed to increase the angular resolution of HARDI or QBI [1][2]. However, there is no deconvolution method directly applied to diffusion ODF without resorting to spherical decomposition. In this study, we developed a deconvolution method that could be directly applied to diffusion ODF, thus extending its applicability to other q-space methods such as DSI and generalized q-space imaging (GQI) [3]. Moreover, this proposed method attempts to minimize the isotropic background effect, which was reported to degrade the result of spherical deconvolution [4]. To test the performance of the proposed method, it was applied to QBI, DSI, and GQI to present the fiber ODFs. Also, the fiber ODFs in gray matter was also presented to demonstrate its resistance to the isotropic background effect. Methods The proposed method first estimates the single fiber diffusion ODF, which is then normalized and used as the deconvolution kernel. The relation between single fiber diffusion ODF Ψs and overall diffusion ODF Ψd can be formulated as follows: (1) where fi is the volume fraction, Ri the rotation matrix, and Ψ0 the isotropic background with the volume fraction of f0. Before deconvolution, the isotropic component of the diffusion ODF is temporarily extracted so that the effect of isotropic background could be minimized. We used the minimum value of the diffusion ODF min(Ψd) as an approximation to the isotropic component f0Ψ0. Then Eq. (1) can be formulated as the convolution form. (2) The fiber ODF Ψf can be estimated through deconvolution with Tikhonov’s regularization. After the deconvolution, the extracted isotropic component is added back to reflect the partial volume condition, resulting in the overall fiber ODF Ψf * as