Alternative Definition
An alternative definition of SNR is as the reciprocal of the coefficient of variation, i.e., the ratio of mean to standard deviation of a signal or measurement:
where is the signal mean or expected value and is the standard deviation of the noise, or an estimate thereof. Notice that such an alternative definition is only useful for variables that are always non-negative (such as photon counts and luminance). Thus it is commonly used in image processing, where the SNR of an image is usually calculated as the ratio of the mean pixel value to the standard deviation of the pixel values over a given neighborhood. Sometimes SNR is defined as the square of the alternative definition above.
The Rose criterion (named after Albert Rose) states that an SNR of at least 5 is needed to be able to distinguish image features at 100% certainty. An SNR less than 5 means less than 100% certainty in identifying image details.
Yet another alternative, very specific and distinct definition of SNR is employed to characterize sensitivity of imaging systems; see signal to noise ratio (imaging).
Related measures are the "contrast ratio" and the "contrast-to-noise ratio".
Read more about this topic: Signal-to-noise Ratio
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