Indirect Fourier transform
Encyclopedia
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.
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.
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
of extremely noisy data (as from biological small-angle scattering) proposed by Glatter.
Transform is computed by linear fit
Linear least squares
In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model...
to a family of functions corresponding to constraints on the reasonable solution.
If a result of the transform is distance distribution function
Radial distribution function
In statistical mechanics, a radial distribution function , g, describes how the atomic density varies as a function of the distance from one particular atom....
, 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.