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We propose a novel fast and analytical method to obtain the orientation distribution function (ODF) from diffusion weighted signals measured using the Q-ball imaging methodology. Past work has involved using the spherical harmonics or radial basis functions to represent the ODF. In this work, we propose to use the hyperspherical de la Vallee Poussin kernel to represent the measured Q-ball signal and derive its spherical radon transform to analytically compute the corresponding ODF. To minimize the number of coefficients used to represent the resulting ODF, we use the matching pursuit algorithm. In particular, we show how to extract principal diffusion directions that are separated by as small as 22.5 degrees in orientation. We show, with experiments, the robustness of the proposed method to signal noise and compare it with ODF computation using spherical harmonics on some synthetic and real data set. The proposed method is particularly useful in applications like tractography, segmentation or for better visualization of principal diffusion directions.