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An algorithm for reconstructing images of reflectors from echo signals that propagate in a test object, which consists of several regions with different acoustic properties, is considered. The ray trajectories are calculated using the method of direct construction of the family of rays that escape from the point where a transmitter is located but not the Fermat variational principle. After the family of rays is constructed, their belonging to a certain acoustic scheme can be analyzed and the approximation of the calculated delays on the spatial mesh of the image reconstruction region (IRR) can be performed. This will allow the reconstruction of both the pulse travel time from the transmitter to any point in the IRR and back to the receiver and the attenuation of the pulse amplitude caused by the divergence, reflection, and refraction effects at the boundaries of the regions that constitute the test object. Numerical and model experiments show the working capacity of the proposed algorithm for reconstructing reflector images. [ABSTRACT FROM AUTHOR]