A constant-variance Gaussian camera twin of Poisson photon counting: which dark/bright decision rule does it teach, and what does that cost on the real sensor?

research/shot-twin

Constant-variance Gaussian camera twin of Poisson photon counting: the real Bayes threshold is the logarithmic mean, the twin's the arithmetic mean (7.28 vs 8.00 for 4 vs 12), a detector tuned in it has 1.25–1.83× the optimal error and 23× at λ0=200 (λ1=2λ0), and a square-root twin recovers the optimum in 8 of 9 pairs. Stylised.

7 tests

What it found

For Poisson counts the Bayes dark/bright threshold is the logarithmic mean (λ₁−λ₀)/ln(λ₁/λ₀); a Gaussian twin with one matched variance puts it at the arithmetic mean (7.28 vs 8.00 for 4 vs 12), and a square-root twin lands in between at (A+G)/2. A detector tuned in the arithmetic twin has 1.25× the optimal real error at (4,12), 1.83× at (10,30) and 1.74× at (50,100), and with λ₁=2λ₀ the penalty grows to 23× at λ₀=200, while the twin’s own predicted error stays within 1.8× of the optimum; the square-root rule recovers the optimal integer rule in 8 of 9 pairs. Stylised: ideal Poisson counts, no read noise, no camera data.

A figure from its own output

Figure produced by research/shot-twin: rule_error — shot-twin/experiments/rule_error.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.