Application of linear prediction and singular value decomposition (LPSVD) to determine NMR frequencies and intensities from the FID

Abstract

A parametric spectral analysis based on linear prediction and singular value decomposition has been applied to the 31P FID of a tumor implanted in a mouse. It is found that a number of complications that may arise in in vivo FFT NMR can be circumvented. The new method yields all parameters of the spectral components, i.e., the frequency, amplitude, damping constant, and phase.

NMR data processing using iterative thresholding and minimum l1-norm reconstruction

“…Let F be the (N × N) unitary matrix corresponding to the DFT, and let K be the (M × N) projection matrix which shortens an N-element vector to its first M elements. Then [8] and [9] where † denotes the Hermitian transpose; F † corresponds to the IDFT and K † corresponds to zero-filling.…”

“…[2] by setting [13] The corresponding modification to Eqs. [8] and [9] simply involve setting the diagonal elements of the matrix K equal to w. The only change needed in IST is to adjust the replacement operation so that it coincides with motion opposite the gradient of the revised constraint. In operator notation, this becomes [14] where the weight operator corresponds to pointwise multiplication by the decay w.…”

“…Procedures adopted from fields outside of NMR have proven to be superior to the discrete Fourier transform (DFT) [1,2]; examples include maximum entropy (MaxEnt) [3,4] and minimum-area [5] reconstruction, maximum likelihood reconstruction (MLM) [6,7], and matrix methods such as LPSVD [8] and HSVD [9]. A method that is conceptually simpler and easier to implement than these methods is iterative thresholding [10][11][12].…”

Ultrafast Excited State Intramolecular Proton Transfer Dynamics of 1-Hydroxyanthraquinone in Solution

“…These oscillations in the TRF of the reaction product arise, since the ESIPT reaction can act as impulsive excitations to some low frequency vibrations. Linear prediction singular value decomposition (LPSVD) 26 and fast Fourier transform (FFT) methods were used to analyze the signals. LPSVD results are listed in Table 2.…”

Suppression of spectral anomalies in SSFP-NMR signal by the Krylov Basis Diagonalization Method

“…In this context, we believe that several other available methods can be used to achieve the same proposed goals of this work. If we consider only those black box type methods; Linear Prediction based methods, like LPSVD [18] and, also, HSVD [19] have proven to be excellent alternatives. Similarly to the KBDM these methods attempt to fit the full spectrum in one shot, being prohibitive expensive for large data sets.…”