Biomedical subjects

V A Mandelshtam

Publications and source records attributed to V A Mandelshtam.

6 recordsLinked to original sources

PubMed2001

Pseudotime Schrödinger equation with absorbing potential for quantum scattering calculations.

The Schrödinger equation (Hpsi) (r) = [E+u(E)W(r)]psi(r) with an energy-dependent complex absorbing potential -u(E)W(r), associated with a scattering system, can be reduced for a special choice of u(E) to a harmonic inversion problem of a discrete pseudotime correlation function y(t) = phi(T)U(t)phi. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only approximately t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.

Journal Article↗

PubMed2001

The extended Fourier transform for 2D spectral estimation.

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals.

Journal Article↗

PubMed2000

The multidimensional filter diagonalization method.

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various "ersatz" or "hybrid" spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N(total) = N(1) x N(2) x vertical ellipsis x N(D), where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357-366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.

Image Processing, Computer-Assisted↗

PubMed2000

The multidimensional filter diagonalization method.

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343-356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained by conventional phase-sensitive FT processing, and correlation peaks in heteronuclear and homonuclear experiments can be condensed to sharp singlets, removing all spin-spin couplings. Examples of singlet-HSQC and singlet-TOCSY spectra show big gains in resolution. It is not necessary to have a finely digitized spectrum, in which the individual multiplet components are resolved, for the methods to work. Examples of FDM spectra, ranging from simple organic molecules and steroids to metalloproteins, are shown.

Artifacts↗

PubMed1999

Pure absorption electron spin echo envelope modulation spectra by using the filter-diagonalization method for harmonic inversion.

Harmonic inversion of electron spin echo envelope (ESEEM) time-domain signals by filter diagonalization is investigated as an alternative to Fourier transformation. It is demonstrated that this method features enhanced resolution compared to Fourier-transform magnitude spectra, since it can eliminate dispersive contributions to the line shape, even if no linear phase correction is possible. Furthermore, instrumental artifacts can be easily removed from the spectra if they are narrow either in time or frequency domain. This applies to echo crossings that are only incompletely eliminated by phase cycling and to spurious spectrometer frequencies, respectively. The method is computationally efficient and numerically stable and does not require extensive parameter adjustments or advance knowledge of the number of spectral lines. Experiments on gamma-irradiated methyl-alpha-d-glucopyranoside show that more information can be obtained from typical ESEEM time-domain signals by filter-diagonalization than by Fourier transformation.

Absorption↗

PubMed1998

Reference deconvolution, phase correction, and line listing of NMR spectra by the 1D filter diagonalization method.

We describe a new way to attack the problem of identifying and quantifying the number of NMR transitions in a given NMR spectrum. The goal is to reduce the spectrum to a tabular line list of peak positions, widths, amplitudes, and phases, and to have this line list be of high fidelity. In this context "high fidelity" means that each true NMR transition is represented by a single entry, with no spurious entries and no missed peaks. A high fidelity line list allows the measurement of chemical shifts and coupling constants with good accuracy and precision and is the ultimate in data compression. There are two parts to the problem. The first is to overcome common imperfections: the non-Lorentzian lineshapes that can arise whenever the magnetic field inhomogeneity is less than perfect, and nonzero time delays that cause frequency-dependent phase errors. The second is to fit the spectral features to a model of Lorentzian lines. We use the recently developed filter diagonalization method (FDM) to accomplish the reference deconvolution, the phase correction, and the fitting, and show good progress toward the goal of obtaining a high fidelity line list.

Fourier Analysis↗