Fast Acquisition for Quantitative MRI Maps: Sparse Recovery from Non-Linear Measurements

This work addresses the problem of estimating proton density and T1 maps from two partially sampled K-space scans such that the total acquisition time remains approximately the same as a single scan. Existing multi-parametric non-linear curve fitting techniques require a large number (8 or more) of echoes to estimate the maps - resulting in prolonged (clinically infeasible) acquisition times. Our simulation results show that our method yields very accurate and robust results from only two partially sampled scans (total scan time being the same as a single echo MRI). We model PD and T1 maps to be sparse in some transform domain. The PD map is recovered via standard Compressed Sensing based recovery technique. Estimating the T1 map requires solving an analysis prior sparse recovery problem from non-linear measurements, since the relationship between T1 values and intensity values / K-space samples is not linear. For the first time in this work, we propose an algorithm for analysis prior sparse recovery for non-linear measurements. We have compared our approach with the only existing technique based on matrix factorization from non-linear measurements, our method yields considerably superior results.