title: Matrix factorization from non-linear projections: application in estimating T2 maps from few echoes.
abstract: 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.
authors.affiliation: Indraprastha Institute of Information Technology, Delhi. Electronic address: prerna1487@iiitd.ac.in.
authors.forename: Prerna
authors.initials: P
authors.lastname: Khurana
authors.affiliation: Indraprastha Institute of Information Technology, Delhi. Electronic address: protim1488@iiitd.ac.in.
authors.forename: Protim
authors.initials: P
authors.lastname: Bhattacharjee
authors.affiliation: Indraprastha Institute of Information Technology, Delhi. Electronic address: angshul@iiitd.ac.in.
authors.forename: Angshul
authors.initials: A
authors.lastname: Majumdar
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Matrix factorization; Non-linear measurement; Quantitative MRI; T2 imaging