Image quality in single photon emission computed tomography (SPECT) is substantially influenced by scatter and a finite volume of response associated with single detector elements. These effects are not restricted to the image plane, implying a shift in the tomographic imaging paradigm from 2D to 3D. The application of a 3D reconstruction model suffers from huge numerical efforts, affording for high performance computing hardware. A novel accelerated 3D ML-EM type reconstruction algorithm is developed by the implementation of a dual projector back-projector pair. An accurate 3D model of data acquisition is developed considering scatter and exact scanner geometry in opposite to a simple pencil-beam back-projection operator. This dual concept of projection and back-projection substantially accelerates the reconstruction process. Speed-up factors achieved by the novel algorithm are measured for several matrix sizes and collimator types. Accuracy of the accelerated reconstruction algorithm is shown by reconstruction of data from a physical Jaszczak phantom and a clinical endocrine study. In both cases the accelerated 3D reconstruction method achieves better results. The novel algorithm has a great potential to scale fully 3D reconstruction down to desktop applications, especially with the new possibilities employing massive parallel graphics hardware. The presented work is a step towards establishing sophisticated 3D reconstruction in a clinical workflow.