Two-dimensional structure reconstruction with expectation and maximization algorithm

In this report, we applied expectation and maximization (EM) method described by Philips et al [1] to recover two-dimensional (2D) structure from multiple sparse signal images in random orientation. The detailed derivation of EM algorithm for 2D image reconstruction was evaluated. Data sets with average 40 photons per frame were successfully classified by orientation. And the 2D mask structure is reconstructed by merging all frames with the appropriate rotations applied to each one. It provides us an alternative approach in data set classification and structural information recovery from extremely weak signal with incomplete information.