Uniqueness for the attenuated x-ray transform in the physical range

The author studies the uniqueness problem for the attenuated x-ray transform of single-photon emission tomography (SPECT). It is shown that when the attenuation coefficient is smooth the attenuated x-ray transform of a compactly-supported density function uniquely determines the density, provided the product of the diameter of the support of the density and the maximum of the attenuation coefficient is less than 5.37. For the attenuation coefficients relevant to SPECT this gives uniqueness for objects with diameters less than 35.8 cm. This is an improvement over previous work in that no bound on derivatives of the attenuation coefficient is required.