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---
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title: SNR_star – Covariance-based SNR measurement
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title: SNR_star – Covariance-based SNR measurement (ImageJ macro)
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categories: [Analysis]
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tags: [SNR, image quality, CT, covariance, ImageJ macro]
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author: Motohiro TABUCHI
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doi: 10.6009/jjrt.2022-1154
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---------------------------
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# SNR_star – Covariance-based SNR measurement
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**Author:** Motohiro TABUCHI
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SNR_star is an ImageJ macro that estimates signal variance and noise variance using the covariance between two repeated images acquired under identical imaging conditions.
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It provides an unbiased and statistically optimal estimation of signal-to-noise ratio (SNR).
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The method is particularly useful for image quality evaluation in X-ray CT where direct measurement of signal variance is difficult.
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---
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## Principle
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SNR* estimates the signal variance from the covariance between two observed images acquired under identical imaging conditions.
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Signal variance:
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σ_s² = Cov(I₁, I₂)
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Noise variance:
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σ_n² = Var(I₁ − I₂) / 2
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The SNR* value in decibels is defined as
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SNR* [dB] = 10 log10 (σ_s² / σ_n²)
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![Principle](./snr_star_principle.jpg)
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---
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## Features
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* Covariance-based signal variance estimation
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* Noise variance estimation from the difference of images
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* Outputs SNR* [dB], ROI size, signal variance, and noise variance
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* Simple workflow using standard ImageJ ROI tools
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* Suitable for quantitative image quality evaluation
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---
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## Requirements
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* ImageJ 1.53 or later
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* Two observed images of identical dimensions
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* Images must be acquired under identical imaging conditions
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---
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## Usage
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![Usage](./snr_star_usage.jpg)
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1. Prepare a folder containing two observed images
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2. Open the first image in ImageJ
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3. Draw a region of interest (ROI)
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4. Run the SNR_star macro
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5. The macro outputs the following values in the Log window:
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* SNR* [dB]
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* ROI size
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* signal variance
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* noise variance
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---
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## SNR_star – Covariance-based SNR measurement
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## Video
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Author: Motohiro TABUCHI
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Demonstration of the SNR* tool:
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SNR_star is an ImageJ macro that estimates signal variance and noise variance using covariance between two repeated images acquired under identical imaging conditions.
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It provides an unbiased and statistically optimal estimation of SNR.
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https://youtube.com/shorts/qBz2MlNHiCE
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### Features
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---
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- Covariance-based signal variance estimation
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- Noise variance estimation from difference of images
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- Outputs SNR* [dB], ROI size, signal variance, and noise variance
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- Simple workflow using ImageJ ROI tools
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## Download
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### Requirements
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GitHub repository
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- ImageJ 1.53 or later
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- Exactly two observed images of identical dimensions acquired under identical imaging conditions
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https://github.com/Motohiro-TABUCHI/SNR_star_Tool
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### Download
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Archived release (Zenodo)
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[GitHub Repository](https://github.com/Motohiro-TABUCHI/SNR_star_Tool)
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https://zenodo.org/record/18666471
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### Notes
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---
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## Notes
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- Assumes additive, zero-mean, independent noise between the two images
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- Larger ROIs improve estimation stability
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- Negative covariance may indicate unsuitable imaging conditions
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* The method assumes additive, zero-mean, independent noise between the two images
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* Larger ROIs improve estimation stability
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* Negative covariance may indicate unsuitable imaging conditions
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* The method is applicable to CT and other imaging modalities with repeated acquisitions
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---
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### Reference
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## Reference
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{% include citation %}

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