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In diffusion-weighted imaging (DWI), reliable fiber tracking results rely on the accurate reconstruction of the fiber orientation distribution function (fODF) in each individual voxel. For high angular resolution diffusion imaging (HARDI), deconvolution-based approaches can reconstruct the complex fODF and have advantages in terms of computational efficiency and no need to estimate the number of distinct fiber populations. However, HARDI-based methods usually require relatively high b-values and a large number of gradient directions to produce good results. Such requirements are not always easy to meet in common clinical studies due to limitations in MRI facilities. Moreover, most of these approaches are sensitive to noise. In this study, we propose a new framework to enhance the performance of the spherical deconvolution (SD) approach in low angular resolution DWI by employing a single channel blind source separation (BSS) technique to decompose the fODF initially estimated by SD such that the desired fODF can be extracted from the noisy background. The results based on numerical simulations and two phantom datasets demonstrate that the proposed method achieves better performance than SD in terms of robustness to noise and variation in b-values. In addition, the results show that the proposed method has the potential to be applied to low angular resolution DWI which is commonly used in clinical studies.