Indirect Fourier transform

Indirect Fourier transform is a solution of ill-posed given by Fourier transform of extremely noisy data (as from biological small-angle scattering) proposed by Glatter.[1]

Transform is computed by linear fit to a family of functions corresponding to constraints on the reasonable solution. If a result of the transform is distance distribution function, it is common to assume that the function is non-negative, and is zero at P(0) = 0 and P(Dmax) ≥ 0, where Dmax is a maximum diameter of the particle. It is approximately true, although it disregards inter-particle effects.

IFT is also performed in order to regularize noisy data.[2]

References

  1. ^ O. Glatter (1977). "A new method for the evaluation of small-angle scattering data". Journal of Applied Crystallography 10: 415–421. 
  2. ^ A. V. Semenyuk and D. I. Svergun (1991). "GNOM – a program package for small-angle scattering data processing". Journal of Applied Crystallography 24: 537–540. doi:10.1107/S002188989100081X.