Estimating fiber orientation distribution from diffusion MRI with spherical needlets

•Novel application of a multiresolution spherical basis to fiber orientation distribution (FOD) estimation from diffusion MRI data.•Excellent localization of FOD peaks and a stable and parsimonious representation of FOD.•Gain estimation accuracy and achieve bias-variance trade-off by sparsity and nonnegativity constraints.•Superior accuracy and robustness over competing techniques and the ability to resolve crossing at angles as small as 30°.