under practical limitations. Both algorithms are quite similar, with
the only difference being the ﬁltering of each individual projection
added to the original procedure in the later method — seemingly an
elementary step, but probably impossible to discover without the
involved theory. The alternative methods of image reconstruction
from projections rely heavily on other aspects of the multidimen-
sional signal theory as well.
Part I introduces the basic image processing concepts and ter-
minology needed to understand further sections of the book. Broader
and deeper treatment of the theory can be found in the numerous
literature that is partly listed in the references to this section,
e.g., in , , , , , , , . Other sources used but
not cited elsewhere are , , , , –, , , .
In context of the theoretical principles, we shall introduce the
concepts of two-dimensional systems and operators, two-dimensional
transforms, and two-dimensional stochastic ﬁelds. The text is con-
ceived to be self-contained: the necessary concepts of the one-dimen-
sional signal theory will be brieﬂy included, however, without detailed
derivations. A prior knowledge of the signal theory elements, though
deﬁnitely advantageous, is thus not necessary. With respect to the
purpose of the book, we shall mostly limit ourselves to the two-dimen-
sional case; the generalization to three- and four-dimensional cases is
rather straightforward and will be mentioned where necessary.