The image quality of FBP and MLEM reconstruction.

We have developed an image quality theory for filtered back-projection (FBP) and maximum likelihood expectation maximization (MLEM) based on quality measures like signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), signal and noise power spectra and the detective quantum efficiency (DQE) concept. Analytic expressions are derived for unattenuated SPECT reconstruction with ideal collimation to obtain the fundamental performance parameters of different reconstruction algorithms. This theory is verified by measurements of signal and noise power on simulated phantoms. We demonstrate that the noise power of reconstructed images is proportional to the diameter of the object given as a number of voxels. This is analytically proven for FBP and clarified by assessment of the convergence properties for MLEM. The latter technique is shown to be superior to FBP in terms of a noise level at least two times lower. The free choice of MLEM reconstruction parameters and correction for physical effects in the image acquisition enables quantitative evaluation of SPECT and PET images.