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## The Anscombe Transform
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The Anscombe Transform is a variance-stabilizing transformation specifically designed for data with Poisson noise. In photon-limited imaging, the noise variance equals the signal mean (characteristic of Poisson statistics), which makes compression difficult because different intensity levels have different noise characteristics.
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The Anscombe Transform is a variance-stabilizing transformation specifically designed for data with Poisson noise. In photon-limited imaging, the noise variance grows linearly with the signal mean (characteristic of Poisson statistics),
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which makes compression difficult because different intensity levels have different noise characteristics.
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### The Problem
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### Accuracy
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The codec is designed to be **nearly lossless** for photon-limited data:
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-Typical error: < 1 photon per pixel
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- Error scales with `conversion_gain` and quantization (`beta` parameter)
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- For well-chosen parameters, reconstruction error is below the noise floor
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-Max absolute error: ~ 0.25 noise-sigma per pixel (for `beta=0.5`)
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- Error scales with quantization (`beta` parameter)
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- For default parameters (`beta=0.5`), the noise variance is increased by a ~1 % with respect to the original noise variance and no bias is introduced.
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## When to Use This Codec
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### Not Recommended ❌
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- Data without Poisson noise (e.g., pre-processed images)
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- Data where camera parameters are unknown and can't be estimated
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- Data with very high dynamic range (> 16-bit)
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- Data that has already been normalized or transformed
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- Data with non-Poisson or non-stationalry noise (e.g., pre-processed images)
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- Data where detector parameters are unknown and can't be estimated
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- Data that has been transformed with a non-linear function (e.g. gamma correction)
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