The present disclosure relates to systems and methods for determining quantitative chemical exchange or exchangeable proton information from a region-of-interest in a subject. The methods and systems use adaptive fitting to quantify magnetic resonance (MR) data, such as chemical exchange saturation transfer magnetic resonance imaging (CEST MRI) images, using initial values based on, for example, Lorentzian fitting. Images are iteratively less downsampled until quantitative maps of desired resolution are obtained. Such an approach allows for reliable fitting at a faster fitting speed, and is less susceptible to suboptimal signal to noise (SNR) than conventional methods.