A Volterra integral equation, which relates the Fourier coefficients of the projection (in polar coordinates) with the corresponding coefficients of the unknown density function, is deduced. The same equation holds for both divergent and parallel beam projections. The problem is shown to be 'ill-conditioned'. A numerical solution, based on the recursive evaluation of certain integrals, is proposed and a Tikhonov regularization procedure is applied to the discete problem. Numerical examples are also reported.
'ILL-CONDITIONED' VOLTERRA INTEGRAL EQUATION RELATED TO THE RECONSTRUCTION OF IMAGES FROM PROJECTIONS
Alliney S.;Sgallari F.
1984
Abstract
A Volterra integral equation, which relates the Fourier coefficients of the projection (in polar coordinates) with the corresponding coefficients of the unknown density function, is deduced. The same equation holds for both divergent and parallel beam projections. The problem is shown to be 'ill-conditioned'. A numerical solution, based on the recursive evaluation of certain integrals, is proposed and a Tikhonov regularization procedure is applied to the discete problem. Numerical examples are also reported.File in questo prodotto:
Eventuali allegati, non sono esposti
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
