Description
Tomographic
imaging is a widespread technique used in many scientific areas,
mainly in medicine and archeology. The data (projections) can be acquired
with transmission techniques (TAC) or with emission techniques (Positron
Emission Tomography PET or Single Photon Emission Tomography SPECT). The
imaging methods present on the commercial systems are not completely satisfactory,
especially in the 3D case.
The project is concerned with the study and development of algorithms for
the reconstruction of images from tomographic projections in the 2D and
in the 3D.
Main
results
We
have considered algebraic imaging reconstructions with iterative methods.
In
the algebraic approach, it is possible, by using a suitable kernel function
in the modelling equation, to consider the distorsion effects and the scattering
of particles (in SPECT and PET).
The
linear systems are solved with conjugate gradient type methods, that are
the most suitable for their computational efficiency when dealing with
large, sparse matrix and for their semiconvergence properties in
the presence of ill conditioning, as this is the case.Particular
care is given to the study of suitable stopping
criteria
for these methods when the problem is ill-conditioned.
Some example:
Data
acquired :64x64x90 bins
Method:Tikhonov+CG
7 iterations
Collaborations
·Dr.
Davide Romani, Department of Physics, University of Bologna.
·Dr.
A. R. Formiconi , Dept. of Clinical Pathophysiology, University of
Florence (ITALY).
·E.
Loli Piccolomini, F. Zama, Parallel
Application on SPECT Data Reconstruction, Progress in
Industrial Mathematics at ECMI98, (edited by L. Archryd,J. Bergh, P. Brenner,
R. Pettersson),Teubner Stuttgrat,Leipzig,1999.
·E.
Loli Piccolomini, F. Zama, Regularization algorithms for image
reconstruction from projections, Series on Advances in Mathematics
for Applied Sciences, (edited by P. Ciarlini, M.G.Cox, F. Pavese, D. Richter),
World Scientific,vol. 45, 1997
