Block-iterative image reconstruction methods, such as ordered subset expectation maximization (OSEM), are commonly used to accelerate image reconstruction. In OSEM, the speed-up factor over maximum likelihood expectation maximization (MLEM) is approximately equal to the number of subsets in which the projection data are divided. Traditionally, each subset consists of a couple of projection views, and the more subsets are used, the more the solution deviates from MLEM solutions. We found for multi-pinhole single photon emission computed tomography (SPECT) that even moderate acceleration factors in OSEM lead to inaccurate reconstructions. Therefore, we introduce pixel-based ordered subset expectation maximization (POSEM), which is based on an alternative subset choice. Pixels in each subset are spread out regularly over projections and are spatially separated as much as possible. We validated POSEM for data acquired with a focusing multi-pinhole SPECT system. Performance was compared with traditional OSEM and MLEM for a rat total body bone scan, a gated mouse myocardial perfusion scan and a Defrise phantom scan. We found that POSEM can be operated at acceleration factors that are often an order of magnitude higher than in traditional OSEM.