### Abstract

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the second spatial derivatives of the reconstructed image pixel intensities. The balance between these two terms is set by a bootstrapping technique where the target value of the log-likelihood term is deduced from a smoothed version of the original data. When compared to the original data, the processed images exhibit lower residuals with respect to the true object. We use photon-sparse data from two different experimental systems, one system based on a single-photon, avalanche photo-diode array and the other system on a time-gated, intensified camera. However, this same processing technique could most likely be applied to any low photon-number image irrespective of how the data is collected.

Original language | English |
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Article number | 42164 |

Journal | Scientific Reports |

Volume | 7 |

DOIs | |

Publication status | Published - 7 Feb 2017 |

### ASJC Scopus subject areas

- General

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## Cite this

*Scientific Reports*,

*7*, [42164]. https://doi.org/10.1038/srep42164