The choice of local HARDI reconstruction technique is crucial for discerning multiple fiber orientations, which is itself of substantial importance for tractography, and reliable and accurate assessment of white matter fiber geometry. Due to the complexity of the diffusion process and its milieu, distinct diffusion compartments can have different frequency signatures, making the HARDI signal spread over multiple frequency bands. Therefore, we put forth the idea of multiscale analysis with localized basis functions, ensuring that different frequency ranges are probed. With the aim of truthful recovery of fiber orientations, we reconstruct the orientation distribution function (ODF), by incorporating a spherical wavelet transform (SWT) into the Funk–Radon transform. First, we apply and validate our proposed SWT method on real physical phantoms emulating fiber bundle crossings. Then, we apply the SWT method to a real brain data set. The analysis of the real data set suggests that different angular frequencies may capture different information, thus stressing the importance of multiscale analysis. For both phantom and real data, we compare the SWT reconstruction with state-of-the-art q-ball imaging and spherical deconvolution reconstruction methods. We demonstrate the algorithm efficiency in diffusion ODF denoising and sharpening that is of particular importance for applications to fiber tracking (especially for probabilistic approaches), and brain connectome mapping. Also, the algorithm results in considerable data compression that could prove beneficial in applications to fiber bundle segmentation, and for HARDI based white matter morphometry methods.