Аннотация:The development of new methods for reconstruction of an object image given its sinogram and some additional information about the object is important due to the possibility of artifact presence in the reconstructed image or its insufficient sharpness when the used additional information does not hold. A new method for processing tomographic images based on combining an assumptions-free image of the object and a dummy estimate followed by projection onto the set of images of possible objects is proposed and developed for the case when this set is the non-negative cone. This additional information corresponds to the natural condition of non-negativeness of the estimated brightnesses. The proposed method with different used iterative solving method and its parameters is illustrated by examples of processing teeth sinograms.