Multiresolution hierarchical blind recovery of biochemical markers of brain cancer in MRSI

We present a multi-resolution hierarchical application of the constrained non-negative matrix factorization (cNMF) algorithm for blindly recovering constituent source spectra in magnetic resonance spectroscopic imaging (MRSI). cNMF is an extension of non-negative matrix factorization (NMF) that includes a positivity constraint on amplitudes of recovered spectra. We apply cNMF hierarchically, with spectral recovery and subspace reduction constraining which observations are used in the next level of processing. The decomposition model recovers physically meaningful spectra which are highly tissue-specific, for example spectra indicative of tumor proliferation, given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the decomposition procedure on ¹H long TE brain MRS data. The results show recovery of markers for normal brain tissue, low proliferative tissue and highly proliferative tissue. The coarse-to-fine hierarchy also makes the algorithm computationally efficient, thus it is potentially well-suited for use in diagnostic work-up.