Image reconstruction from photon sparse data.
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.
School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK.
Lena
L
Mertens
School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK.
Matthias
M
Sonnleitner
Department of Physics, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
Jonathan
J
Leach
Department of Physics, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
Megan
M
Agnew
School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK.
Miles J
MJ
Padgett