Assuming the density function is of the form f(x) = Sigma(j=1)(m)c(j)
delta(x - x(j)) and the sinogram Rf(alpha, p) is known for all alpha e
psilon S-1 and p epsilon R, we give methods for finding c(j) and x. Fi
rst we consider the case where the locations x(j), j = 1, ..., m, are
known. The value of c(j) is estimated from q(alpha) := integral(-infin
ity)(+infinity)(Rf)(alpha, p)h(p) dp, where h is a function and alpha
is a non-degenerated projection direction such that alpha.x(j) not equ
al alpha.x(i) for j not equal i. Then we derive a method for the gener
al case: the number m of S functions, their localization and their int
ensity are estimated from the data Rf(alpha, p). We show that this new
method is more efficient than the filtered backprojection when the re
solution in the variable p of the sinogram is high.