Abstract:
The present disclosure provides a semi-analytic inversion method that computes an approximate, sparse representation of the data in terms of the (a, T1, T2). Methods, in accordance with the present disclosure, compute T2's in a semi-analytic fashion, such as by using simultaneous Hankel representation of the data, use one dimensional convex optimization to compute the amplitudes, a, and finally compute T1 in an analytic fashion by appropriate averaging techniques. The proposed method provides a more efficient way to represent the data when compared to linearized methods, and is computationally less demanding when compared to some existing nonlinear optimization methods.