A method for the reconstruction of 3-D images, based on the analysis of time–resolved backscattered signals, is described. The method evaluates a linear perturbation equation by a progressive iterative backprojection scheme. A key feature of the method is the use of weighting functions, which estimate the impact that absorption of photons in the interior have on the response of detectors located at the surface. Examples of reconstructed images shown are based on the analysis of simulated data for multilayered media, and simulated and experimental data for media containing finite–volume absorbers. These results contain features that indicate images having high resolution are obtainable even in the limiting case where the view angle is restricted to only backscattered signals and the absorption contrast across an interior boundary is 1%. A general scheme, similar to a layer–stripping approach, is described for the case where signals emerging about a target are measured.