Cardiac gated SPECT is an important clinical tool for assessment of both myocardial perfusion and ventricular function. Spatiotemporal (aka 4D) reconstruction has been demonstrated to be effective for suppressing the increased noise in cardiac gated SPECT. In this work, we propose a joint 4D reconstruction approach to accommodate the different respiratory phases in a dual cardiac-respiratory gating scheme in order to combat the artifacts of respiratory motion in cardiac SPECT. The proposed approach is to exploit the correlation in the signal component among both the cardiac and respiratory phases in the acquired data. In our experiments we evaluated the approach using simulated SPECT imaging with the 4D NCAT phantom and Tc-99m labeled Sestamibi as the imaging agent. Our results demonstrate that the proposed approach could effectively suppress the artifacts caused by respiratory motion in the reconstruction.