A Sparse Representation Method for Magnetic Resonance Spectroscopy Quantification

In this paper, a sparse representation method is proposed for magnetic resonance spectroscopy (MRS) quantification. An observed MR spectrum is composed of a set of metabolic spectra of interest, a baseline and a noise. To separate the spectra of interest, the
a priori
knowledge about these spectra, such as signal models, the peak frequencies, and linewidth ranges of different resonances, is first integrated to construct a dictionary. The separation of the spectra of interest is then performed by using a pursuit algorithm to find their sparse representations with respect to the dictionary. For the challenging baseline problem, a wavelet filter is proposed to filter the smooth and broad components of both the observed spectra and the basis functions in the dictionary. The computation of sparse representation can then be carried out by using the remaining data. Simulation results show the good performance of this wavelet filtering-based strategy in separating the overlapping components between the baselines and the spectra of interest, when no appropriate model function for the baseline is available. Quantifications of
in vivo
brain MR spectra from tumor patients in different stages of progression demonstrate the effectiveness of the proposed method.