The objective of this study was to develop very low noise and high-contrast-to-noise ratio fast proximity algorithm for MAP ECT reconstruction that would allow significant (factor of two or more) patient's dose reduction, as compared to conventional OSEM algorithm. We proposed a semi-dynamic Preconditioned Alternating Projection Algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulated the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We characterized the solution of the constrained convex optimization problem and showed that it satisfies a system of fixed-point equations defined in terms of two proximity operators arising from the convex functions that define the TV-norm and the constrain involved in the problem. We proved theoretically the convergence of the proposed algorithm. For efficient numerical computation, we introduced to the alternating projection algorithm a preconditioning matrix: the EM-preconditioner. In numerical experiments using Monte Carlo simulated SPECT data performance of our algorithms was compared with performance of the conventional EM algorithm with Gaussian postfilter. Based on the results of these experiments, we observed that PAPA algorithm with the EM-preconditioner outperforms very significantly the benchmark EM in terms of contrast-to-noise ratio and the noise characteristics of the reconstructed images.