1. A method for producing a quantitative map of transverse relaxation rate while separating signal contributions from at least two chemical species using a magnetic resonance imaging (MRI) system, the steps of the method comprising: a) acquiring k-space data with the MRI system using a partial k-space acquisition that samples a fraction of k-space, the k-space data corresponding to magnetic resonance signals formed at least at three different echo times; b) producing low-pass filtered data by applying a low-pass filter to the k-space data acquired in step a); c) reconstructing low resolution images from the low-pass filtered data; d) fitting the low resolution images to a signal model to estimate a low resolution field map, a first low resolution image depicting signal contributions from a first chemical species separated from a second chemical species, and a second low resolution image depicting signal contributions from the second chemical species separated from the first chemical species; e) applying a weighting to the k-space data acquired in step a); f) reconstructing weighted images from the weighted k-space data; g) demodulating the weighted images using the low resolution field map, first low resolution image, and second low resolution estimated in step d); h) estimating a transverse relaxation rate, R 2 *, map by fitting the images demodulated in step g) to a signal model that accounts for the demodulation performed in step g), the R 2 * map having a higher spatial resolution than the low resolution images reconstructed in step c); and i) fitting the weighted images reconstructed in step f), the low resolution field map estimated in step d), and the R 2 * map estimated in step h) to a signal model to produce a first image depicting signal contributions from the first chemical species separated from a second chemical species, and a second image depicting signal contributions from the second chemical species separated from the first chemical species, the first and second images having a higher spatial resolution than the first and second low resolution images.