  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 or 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.
