Three-dimensional reconstruction in nuclear medicine by iterative least- squares and fourier transform techniques

Abstract

Quantitative three-dimensional distribution oi isotopes in patients is de termined by digital reconstruction of data from many views taken by rotating the subject at 10' intervals before the gamma camera. The superiority of these techniques over conventional tomography is demonstrated by comparisons between reconstruction algorithms such as back-projection, simultaneous iterative reconstruction, iterative least-squares, and back-projection of filtered projection. The filtered back-projection technique (convolution method) is superior in speed; however, for quantitative results that take into account both noise and attenuation, the iterative least-squares method gives the best approximation to the real source distributions. Resolution is 1.25 cm for detection of holes in 20-cm-diameter objects.Mathematical basis and FORTRAN listings applicable o transmission and emission imaging are given, as well as phantom and patient studies.

The stability analysis of dynamic SPECT systems

“…By Lemma 3.2, we can assume that A A A k1 , A A A k2 and A A A k3 are full rank. Then the submatrix corresponding to the k 1 th, k 2 th and k 3 For this underlying SPECT model, the physical parameters λ and η always satisfy λ i > η i > 0 for each i . Then Φ Φ Φ is full rank if the data collected are large enough.…”

Advanced Data Acquisition Methods for Quantitative Single Photon Emission CT

“…4 and 5. The pixel size is assumed to be 0.5 cm, and the size of the reconstruction area is 64 X 64 pixels so that the real size is 32 X 32 cm2.…”

“…0278-0062/84/1200-0187$01.00 © 1984 IEEE [4] corrects the first term in (7) by multiplying the inverse of the mean of attenuation factor, which is defined as…”

“…Some correction will be necessary when we extract precise quantitative data such as organ volume, lesion size, or regional distribution of functional parameters. A considerable effort has been devoted to the study of attenuation and to the development of correction algorithms; they are, for instance, the analytical method [1], [2], the weighted back projection method [3], and the iterative procedure with minimum error [4]- [8].…”

Using algebraic reconstruction in computed tomography

“…This is a commercial application based on filtered back projections [3]. To reconstruct data from the MARS scanner, each energy bin is reconstructed independently.…”