We address the problem of robust estimation of tissue microstructure from Diffusion Magnetic Resonance Imaging (dMRI). On one hand, recent hardware improvements enable the acquisition of more detailed images, on the other hand, this comes along with a low Signal to Noise (SNR) ratio. In such a context, the approximation of the Rician acquisition noise as Gaussian is not accurate. We propose to estimate the volume of PDF-based characteristics from data samples by minimizing a nonlinear energy functional which considers Rician MR acquisition noise as well as additional spatial regularity constraints. This approach relies on the approximation of the MR signal by a series expansion based on Spherical Harmonics and Laguerre-Gaussian functions. Results are presented to depict the performance of this PDE-based approach on synthetic data and human brain data sets respectively.