Abstarct: Single photon emission computed tomography or SPECT is a nuclear imaging technique that aims to collect information from the imaging tissue by measuring the amount of activity of different pixels of image in the tissue. In this method, the gamma camera is used to record information about photons emitted from radioactive materials in different parts of the tissue. In practice, some of the photons emitted from different regions of the tissue are absorbed by other points or environments that lie in the gamma-to-tissue path. This can cause an error in the estimated values of activity. Also, by the nature of the received photon of count data, we expect overdispersion to exist. For this reason, we use the negative binomial distribution to cover this data feature. Using a new recurrence formula baxsed on the maximum likelihood approach, the actual activity (image) and the absorption (attenuation) coefficients are estimated simultaneously. In practice, the device SPECT/CT is used to receive the revised images, which is worthy and of course, rare in our country. However, SPECT device information is enough to reconstruct the image, only. By applying the proposed method in this research, we do not need the SPECT/CT device.