MPSA is a software package for cryoEM reconstructions based on the common-line method in Fourier space. Originally developed for symmetry-breaking reconstructions of tailed phages, the package is currently capable of asymmetric, symmetry-breaking, and symmetric (such as icosahedral) reconstruction. The software utilizes a Monte Carlo-based optimization algorithm, multi-path simulated annealing, to speed up image processing. The package is capable of simultaneously refining the center, orientation and defocus of a particle image.