Abstract
We employ quantum retrodiction to develop a robust Bayesian algorithm for reconstructing the intensity values of an image from sparse photocount data, while also accounting for detector noise in the form of dark counts. This method yields not only a reconstructed image but also provides the full probability distribution function for the intensity at each pixel. We use simulated as well as real data to illustrate both the applications of the algorithm and the analysis options that are only available when the full probability distribution functions are known. These include calculating Bayesian credible regions for each pixel intensity, allowing an objective assessment of the reliability of the reconstructed image intensity values.
Highlights
Much of what we do in physics and, in other fields is about prediction: we seek to answer questions of the form ‘what will happen if?’
Standard image denoising algorithms result in a single image output, with no metric to enable the user to judge either the quality of the reconstruction as a whole or the ability of the algorithm to deal with specific features within the image
The inherent links with Bayesian inference methods provides a natural framework for constructing an algorithm for analysis of low photocount data that is dominated by Poisson noise
Summary
Much of what we do in physics and, in other fields is about prediction: we seek to answer questions of the form ‘what will happen if?’. To address each of these we start with what we know and try to infer how we got to this situation In this sense they each require retrodiction [1,2,3,4] or postdiction [5], the ability to infer something about the past, rather than prediction of the future. At the heart of our approach is the retrodictive quantum theory of the photodetection process, applied to low light levels [12]. This provides a pre-measurement state based on the number of photocounts registered at a detector.
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