Matrix factorization from non-linear projections: application in estimating T2 maps from few echoes

This work addresses the problem of estimating T2 maps from very few (two) echoes. Existing multi-parametric non-linear curve fitting techniques require a large number (16 or 32) of echoes to estimate T2 values. We show that our method yields very accurate and robust results from only two echoes, where as the curve-fitting techniques require about 16 echoes to achieve the same level of accuracy. We model T2 maps as a rank-deficient matrix. Since the relationship between T2 values and intensity values/K-space samples is not linear, estimating the T2 values requires recovering a low-rank matrix from non-linear projections. We solve this as a non-linear matrix factorization problem. Since the said problem has not been solved before, we propose a simple algorithm for the same.