Imaging of water diffusion using magnetic resonance imaging has become an important noninvasive method for probing the white matter connectivity of the human brain for scientific and clinical studies. Current methods, such as diffusion tensor imaging (DTI), high angular resolution diffusion imaging (HARDI) such as q-ball imaging, and diffusion spectrum imaging (DSI), are limited by low spatial resolution, long scan times, and low signal-to-noise ratio (SNR). These methods fundamentally perform reconstruction on a voxel-by-voxel level, effectively discarding the natural coherence of the data at different points in space. This paper attempts to overcome these tradeoffs by using spatial information to constrain the reconstruction from raw diffusion MRI data, and thereby improve angular resolution and noise tolerance. Spatial constraints are specified in terms of a prior probability distribution, which is then incorporated in a Bayesian reconstruction formulation. By taking the log of the resulting posterior distribution, optimal Bayesian reconstruction is reduced to a cost minimization problem. The minimization is solved using a new iterative algorithm based on successive least squares quadratic descent. Simulation studies and in vivo results are presented which indicate significant gains in terms of higher angular resolution of diffusion orientation distribution functions, better separation of crossing fibers, and improved reconstruction SNR over the same HARDI method, spherical harmonic q-ball imaging, without spatial regularization. Preliminary data also indicate that the proposed method might be better at maintaining accurate ODFs for smaller numbers of diffusion-weighted acquisition directions (hence faster scans) compared to conventional methods. Possible impacts of this work include improved evaluation of white matter microstructural integrity in regions of crossing fibers and higher spatial and angular resolution for more accurate tractography.