A K Louis and Th Schuster 1996 Inverse Problems 12 685 doi:10.1088/0266-5611/12/5/011
A K Louis and Th Schuster
Show affiliationsThe approximate inverse is a method to precompute inversion operators for linear and some special nonlinear problems. In this paper this technique is applied to derive inversion formulae for the parallel geometry in x-ray computerized tomography. The structure of reconstruction formulae is given, and for the case of a finite number of data convolution filters are computed leading to methods of filtered backprojection type. The technique can be extended to treat other scanning geometries. The main advantage is the possibility to precompute the reconstruction kernel independently of the data so that a fast reconstruction is possible.
Issue 5 (October 1996)
Received 6 November 1995, in final form 17 July 1996
A K Louis and Th Schuster 1996 Inverse Problems 12 685
P Jonas and A K Louis 2004 Inverse Problems 20 75
F Schöpfer et al 2006 Inverse Problems 22 311
U Schmitt and A K Louis 2002 Inverse Problems 18 645
Alfred K Louis 2003 Inverse Problems 19 S31
A K Louis 1996 Inverse Problems 12 175
A K Louis and P Maass 1990 Inverse Problems 6 427
Antti Savinainen and Philip Scott 2002 Phys. Educ. 37 45
R Goebel et al 2009 Metrologia 46 01012
O Power and N Fletcher 2008 Metrologia 45 01002