Sunday, July 19, 2020

How many photons does it take to form an image?

ResearchGate: Glasgow University, UK, paper "How many photons does it take to form an image?" by Steven D. Johnson, Paul-Antoine Moreau, Thomas Gregory, and Miles J. Padgetta tries to answer on a somewhat philosophical question:

"If a picture tells a thousand words, then we might ask ourselves how many photons does it take to form a picture? In terms of the transmission of the picture information, then the multiple degrees of freedom (e.g., wavelength, polarization, and spatial mode) of the photon mean that high amounts of information can be encoded such that the many pixel values of an image can, in principle, be communicated by a single photon. However, the number of photons required to transmit the image information is not necessarily, at least technically, the same as the number of photons required to image an object. Therefore, another equally important question is how many photons does it take to measure an unknown image?

For intensity images, it seems that one detected photon per image pixel is a realistic guide, but this may be reduced by making further assumptions on the sparsity of an image in a chosen basis, such as spatial frequency. In this last respect, the advent of machine learning, knowledge-based reconstruction, and similar techniques alleviates the need for a user to explicitly define the sparse basis, but rather the prior is determined from a library of previously recorded images of a similar type. This machine learnt prior can then potentially be designed into the optimum measurement strategy. It seems likely therefore that future imaging systems will combine state-of-the-art single photon detectors with knowledge-based processing both in the design of the system itself and in the processing of the collected data to yield images or decisions based on these data on the basis of extremely low numbers of photons, potentially well below one photon per image pixel.
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Once we are at single-photon imaging, the International SPAD Sensor Workshop (ISSW 2020) held as an on-line event in June published a nice SPAD photon-accumulation video of the city of Edinburgh:

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