摘要： In previous work, we have proposed scatter-to-attenuation reconstruction for positron emission tomography (PET). Scatter-to-attenuation reconstruction aims at recovering object attenuation information in the form of spatial electron-density distributions from pairs of coincident photons, one of which has been single-scattered. One idea is to interleave scatter-to-attenuation reconstruction, which inputs an activity distribution and outputs an attenuation map, with trues-to-activity reconstruction, which inputs said attenuation map and outputs an improved activity distribution. However, major uncertainties regarding the applicability of this approach revolve around a) the unknown impact of the initial activity estimate; b) evaluation of reconstructed activity distributions, and c) convergence to the correct solution. Methods: Using low-dimensional simulated PET data (mouse-sized, 18x18-voxels phantom), we start with mostly uniform initial activity and attenuation estimates and iteratively apply maximum-likelihood expectation-maximization (MLEM) and a maximum-likelihood gradient-ascent (MLGA) algorithm to update activity (from unscattered data) and attenuation (from scattered data), respectively. We evaluate results in terms of log-likelihoods of the expected scatter histograms, and normalized mean squared errors with respect to reference image-space distributions of activity and attenuation. Results: In our study, both attenuation and activity converged to the reference distributions, despite MLEM and MLGA starting with incorrect attenuation and activity estimates, respectively. Conclusion: The MLGA scatter-to-attenuation reconstruction algorithm, in combination with MLEM trues-to-activity reconstruction, jointly reconstructs attenuation maps and attenuation-corrected activity distributions from scattered and unscattered coincidences without reliance on a-priori information about the activity distribution.