Tomographic reconstruction of a region with a given density value

A new tomographic method is proposed to find the object's region filled with a homogeneous substance whose density is given. Its essence is that a pixel of the tomogram is assumed to belong to the image of the region if its brightness lies in a certain interval whose boundaries are determined from the minimum condition for the weighted sum of the error probabilities of the first and second kinds. In order to determine these probabilities, some statistical hypotheses on the distribution of pixel brightness in the reconstructed image are formulated. The adopted hypotheses are confirmed by numerical results.