Restoration when the data is a histogram.

EMCCD imaging is not "image plus noise"

An EMCCD detector operated at high electron-multiplication gain (g in the 100–300 range, used for twilight imaging and for lucky-imaging where individual exposures are sub-second) produces an output that is best described as a stochastic count: at most pixels you see zero photons; at some pixels you see one; at a few pixels you see two or more, with a multiplication-noise factor of √2 stacked on top of the Poisson statistics. The histogram of pixel values across a flat field is bimodal in this regime — a peak at zero and a tail. The point estimate at any single pixel is, in the language an instrument scientist will recognise, not very informative.

This is why a Gaussian-trained denoiser like BM3D produces visually pleasant outputs that quietly bias the photometry. Photon-count statistics are not symmetric around the mean and cannot be smoothed away.

A variational network with a Poisson likelihood layer

Photon's architecture is a variational autoencoder whose decoder includes a custom layer that evaluates the Poisson log-likelihood of the observed integer counts against the predicted intensity. The reconstruction loss is therefore not L2 (the implicit Gaussian-likelihood term in a standard VAE) but the negative log-likelihood of a Poisson distribution at every pixel, with an additional multiplication-noise factor folded into the variance estimate per pixel based on the detector's gain.

The encoder sees small patches (128×128) with a 16-frame stack for lucky-imaging mode and a single frame for twilight calibration mode. The latent prior is a structured Gaussian over latent maps with learned spatial covariance; the network is small (12 M parameters) on purpose so that it overfits less and so that the validation notebook can rerun end-to-end on a single A100 in under twenty minutes.

The 1.7× headline, with caveats

The "effective gain" metric is the inverse of the standard deviation of recovered photometry on a calibrated star field divided by the inverse of the raw-stack standard deviation. The 1.7× figure is at g = 200 on the partner-site EMCCD; at g = 100 the advantage narrows to 1.4×, and at g = 50 Photon is roughly equivalent to a self-supervised baseline.

Where Photon runs today

Two partner observatories. One uses Photon as a twilight-calibration denoiser in the nightly reduction pipeline; the other has it inside a lucky-imaging stack that targets close binary companions. Both installations are owned by the partner and run on their own GPU hardware; we ship a Docker image with the same deterministic build pipeline used for Helios.

A third observatory has the validation notebook and is evaluating Photon against an in-house solution before committing to integration. We do not push on these evaluations; an instrument scientist who has done their own benchmark is the customer we want.

The regimes where Photon is the wrong tool

Photon is not a general image-restoration tool. CCD imaging in the read-noise-limited regime (long exposures, no electron multiplication) is handled better by classical methods or by L2-trained networks; the Poisson likelihood overpenalises in that regime. Photon is also not a deblending tool — overlapping point sources need a different decomposition step before Photon is brought in. Both limitations are documented in the README of the model release on the Data page.