if CT no (HU)=-5 & SD = 6
So SNR = ??? ... let me ask it is accepted to get SNR in negative value ?
The SNR of the image is not the Hounsfield unit. The image SNR is the intensity value of the measured area divided by a modified measure of the variation in the ROI. The Hounsfield unit is a linear transformation that is self referenced in the image and is used to compare images across different CT systems or samples. The calibration values in HU for water is HU=0 where the intensity of the image for the water value is the mean of the ROI. The SD will be the square root of the measured pixel variation in the ROI. If you wanted to combine those two measurements it is possible to include the SD into the HU transformation again a linear scale.
I'm including a link that has a good explaination of HU and the calibration which will enable you to perform your own calculations with a known water and air sample in the image.
https://www.sciencedirect.com/topics/medicine-and-dentistry/hounsfield-scale
I hope this helps with your research.
A frequently used strategy to avoid the technical difficulties with respect to definition and measurement of SNR in CT is to use the contrast-to-noise ratio (CNR) based on the difference of the CT numbers (densities, in HU) of two different tissues or regions. The CNR is generally defined in a straight-forward manner as (HU1 - HU2) / (std.dev. of noise).
[If one insists on using the SNR, one should first define what is meant by "signal" in CT. This should be a quantity proportional to the numbers of photons that hit the detector (i.e. this "signal" should be highest for air and lowest for materials with high absorption). Obviously, this is not the CT number in HU.
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