FINDING SMALL OBJECTS FROM TOMOGRAPHIC DATA

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.