In PET(Positron Emission Tomography), it is necessary to use transmission scan data in order to estimate the attenuation map. Recently, there are several empirical studies in which one might be able to estimate attenuation map and activity distribution simultaneously with emissive sinogram alone without transmission scan. However, their algorithms are based on the model in which does not include the background counts term, and so is unrealistic. If the background counts component has been included in the model, their algorithm would introduce non-monotonic reconstruction algorithm which results in vain in practice. in this paper, we develop a monotonic and parallelizable algorithm for simultaneous reconstruction of both characteristics and present the validity through some simulations.