A wrong diagnosis will occur in cardiac SPECT imaging if the attenuation and scattering of photons by body's soft tissues are not considered. To correct the attenuation, the simultaneous emission and transmission projections must be obtained from the same SPECT system, and attenuation correction algorithms must be used in the emission image reconstruction. This paper compares the qualities of various image reconstruction algorithms in SPECT, such as conventional filtered back-projection, weighted back-projection, iterative Chang's method, ML-EM, OS-EM, RAMLA, ML-EM with Gibbs smoothing and Bayesian reconstruction, etc.. A mathematical phantom is used to test the various algorithms. Some suggestions for choosing the most appropriate algorithm are also put forward. A new algorithm, the Multi-object Optimization Method, is proposed to improve image reconstruction and attenuation correction.