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Q-Ball imaging (QBI) is a successful and widely used high angular resolution diffusion imaging (HARDI) technique which can compute orientation distribution function (ODF). This technique only needs single shell HARDI data and does not require any assumption about the diffusion signal outside the sampling sphere. However the originally proposed ODF (the radial project of the probability density function (PDF)) is not a true ODF. In contrast the marginal ODF with solid angle consideration, represents a true ODF with a correct probabilistic interpretation. In this paper a novel model-free and single-shell HARDI method for analytical reconstruction of the marginal ODF based on Funk-Radon transform (FRT) is proposed. In other words, a transformation of QBI for marginal ODF is proposed in this paper. While there's also a proportional factor introduced by FRT. Its complexity is comparable to that of the original QBI. Finally the present paper verify the algorithm and show the improved result of my method compared to the original QBI on synthetic data, biological phantom data and real human brain data.