Nonlinear Response Theory innD NMR with Complex Stochastic Excitation

Nonlinear Identification of NMR Spin Systems by Adaptive Filtering

“…This does not entail any loss of generality, but the complexity of Eq. [3] is reduced, especially in the case of high-order kernels ( p Ն 3), and consequently the calculation time is considerably reduced.…”

“…Other methods, using a functional expansion, like the Volterra series, to describe the relation between excitation and the nonlinear behavior of the system have appeared (2,3). The system response can, in principle, be written as…”

“…[1] does not lead to orthogonal expansion, the estimation of Volterra kernels from a given excitation-response data set is far from trivial (3,4). Blümich and Ziessow (2) proposed an expansion of the nonlinear system response into a functional integral series with heuristic ansatz for the Volterra kernels.…”

Magnetic resonance fingerprinting review part 2: Technique and directions

“…Randomized sampling was previously used, and is in the spirit of the idea of compressed sensing for MRI . Earlier works, and later, utilized randomized excitation for nuclear magnetic resonance (NMR) spectroscopy. MRF is unique in that the sequence parameters and sampling trajectories are varied together to create spatial and temporal incoherence in the signal evolutions.…”