  Tomographic reconstruction of a binary image from few projections is
considered. A novel {\em heuristic} algorithm is proposed, the central element
of which is a nonlinear transformation $\psi(p)=\log(p/(1-p))$ of the
probability $p$ that a pixel of the sought image be 1-valued. It consists of
backprojections based on $\psi(p)$ and iterative corrections. Application of
this algorithm to a series of artificial test cases leads to exact binary
reconstructions, (i.e recovery of the binary image for each single pixel) from
the knowledge of projection data over a few directions. Images up to $10^6$
pixels are reconstructed in a few seconds. A series of test cases is performed
for comparison with previous methods, showing a better efficiency and reduced
computation times.
