Contrast to Noise Ratio

Estimate signed two-ROI CNR using difference-noise SD/√2 from independent matched acquisitions; unlike reference-ROI contrast metrics, the noise estimate is independent.

Description

CNR measures the signed difference of two regional means relative to estimated single-acquisition noise.

CNR measures the signed difference of two regional means relative to estimated single-acquisition noise. A difference-image SD contains noise from two acquisitions.

The tool returns firstRoiMean (first roi mean); secondRoiMean (second roi mean); singleAcquisitionNoiseSd (single acquisition noise sd); contrastToNoiseRatio (contrast to noise ratio). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.

When to use Contrast to Noise Ratio

Use Contrast to Noise Ratio when you already have firstRoiSignals, secondRoiSignals, noiseDifferenceSignals and want firstRoiMean, secondRoiMean, singleAcquisitionNoiseSd, contrastToNoiseRatio. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.

How to use Contrast to Noise Ratio and understand its results

Enter firstRoiSignals, secondRoiSignals, noiseDifferenceSignals using the field table below. Match the units, ordering and data boundaries described in the calculation.
Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
Read firstRoiMean, secondRoiMean, singleAcquisitionNoiseSd, contrastToNoiseRatio. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.

Input field	Meaning	Value type and bounds	Requirement
firstRoiSignals	First roi signals	list of number	Required
secondRoiSignals	Second roi signals	list of number	Required
noiseDifferenceSignals	Noise difference signals	list of number	Required

Use nonempty ROI signals and at least two varying noise-difference observations. The three list lengths need not match.

noiseSD = sampleSD(difference)/sqrt(2); CNR = (firstMean−secondMean)/noiseSD

The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.

json

{
  "input": {
    "firstRoiSignals": [
      10,
      12
    ],
    "secondRoiSignals": [
      4,
      6
    ],
    "noiseDifferenceSignals": [
      -1,
      1
    ]
  },
  "output": {
    "firstRoiMean": 11,
    "secondRoiMean": 5,
    "singleAcquisitionNoiseSd": 1,
    "contrastToNoiseRatio": 6
  }
}

Limitations and assumptions

The √2 adjustment assumes independent equal-variance acquisition noise and negligible differences from motion or drift.

Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.

Alternative or Complementary methods

SNR From Two Acquisitions: Estimate SNR from matched independent acquisitions using SD(image1−image2)/√2; drift, motion and mismatched anatomy contaminate the noise estimate. Neuromelanin Contrast: Compute neuromelanin-sensitive ROI/reference contrast and CNR using reference sample SD; scanner sequence and ROI selection are external, and contrast is not neuron density.

Methodological background: Measures of scale: sample variance and standard deviation.^[1]

References

Measures of scale: sample variance and standard deviation — NIST/SEMATECH

Similar or alternative tools

SNR From Two Acquisitions
Estimate SNR from matched independent acquisitions using SD(image1−image2)/√2; drift, motion and mismatched anatomy contaminate the noise estimate.
Neuromelanin Contrast
Compute neuromelanin-sensitive ROI/reference contrast and CNR using reference sample SD; scanner sequence and ROI selection are external, and contrast is not neuron density.