# Two-dimensional structure reconstruction with expectation and maximization algorithm

## TL;DR

This paper presents an EM algorithm-based method for reconstructing 2D structures from sparse, randomly oriented images, successfully classifying data and recovering structures from weak signals with incomplete data.

## Contribution

It introduces a detailed EM algorithm derivation for 2D image reconstruction from sparse signals, offering an alternative approach for structural recovery in challenging conditions.

## Key findings

- Successfully classified images with an average of 40 photons per frame
- Reconstructed 2D structures by merging frames with correct rotations
- Provided an effective method for weak signal data classification

## Abstract

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.

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Source: https://tomesphere.com/paper/1701.03022