# How to add noise to a vector-valued simulation?

In past I have added noise to images where % noise is $$\frac{\text{var}(noise)}{\text{var}(image)}$$ easily converted to dB if need be.

I have here a vector valued elasticity simulation I wish to add noise to. Nearly all of the displacement is through one particular plane. So I am not sure taking the variance of the whole data set will give me the right measure, I think it will be too low as the perpendicular displacement components are close to zero. But, it doesn't seem right that the additive noise should be different for each component.

Any suggestions for how to correctly add _% Gaussian noise to this simulation?

• so, you know the Gaussian distribution, hence you know its variance-defining parameter $\sigma$, and you can measure the empirical variance of your image. What's your question? – Marcus Müller Dec 6 '16 at 12:30
• Suppose the power of one component sums to 3 and the power of the others sums to 0. The signal power will be estimated at 1. And maybe this is right. But it seems more intuitive that the power is some sort of Euclidean distance of the 3 components, and the noise measured in relation to this, so that the estimated power is 3. – barnhillec Dec 6 '16 at 14:45
• well, I don't fully understand your problem, so I'd love to see it explained with more background: you have a formula that you need to fulfill that says "take variance of image"; now, I'm no expert in your particular kind of image, but it seems you don't actually want to apply that formula, because you have application-specific concerns regarinding its usefulness. Is that right? – Marcus Müller Dec 6 '16 at 15:05