Nonnegative matrix factorization for tissue mixture modeling with noisy MR magnitude image sequences

Nonnegative matrix factorization (NMF) is a powerful blind source separation method that can be used for nonpara-metric partial volume mixture modeling in a variety of high-dimensional medical imaging experiments. However, conventional NMF methods can fail to produce meaningful results when the measurements contain substantial non-Gaussian noise. This paper proposes a new NMF modeling approach that is appropriate for noisy MRI magnitude images that follow the noncentral chi (NCC) statistical distribution. We formulate a maximum likelihood optimization problem, which we solve by combining conventional least-squares NMF algorithms with a recent majorize-minimize framework for the NCC distribution. This new approach is applied to real diffusion MRI data, and is demonstrated to yield improved results relative to conventional NMF.