Quantification of 1-D and 2-D magnetic resonance time domain signals

Abstract

This paper addresses quantification of uniformly sampled time domain signals by means of State Space modelling (based on Singular Value Decomposition (SVD) and Vandermonde Decomposition). An advantage of State Space modelling is that a specific model function and starting values of model parameters need not be provided by the user. A disadvantage is that if a detailed model function and prior knowledge about model parameters is available, such information cannot be accommodated. Aspects considered are, among other things, 1) Reduction of the computation time of SVD by invoking the Lanczos algorithm and exploiting the Hankel symmetry of the data matrix, 2) Handling of nonexponentially damped signals, 3) Rank-related problems with 2-D signals and their solution. © 1992 IUPAC