As for the variance, if we multiple each Z-value by a constant, the variance increases by the square of that constant. If we add a constant to each Z-value we generated, we effectively change the mean by the constant. This is actually a very simple operation, since we already have a normalized Gaussian distribution. Now, we’d like to be able to change the mean and variance of this distribution so that we can experiment with Gaussian distributions other than just the normalized Gaussian distribution (ie: something other than just mean = 0, variance = 1). Once we’ve generated enough Z-values using these formulae (using different random values for and each time, of course), the Z-values will roughly approximate a normalized Gaussian/normal distribution, according to the central limit theorem.

We can generate from these values, two separate random variables which will approximately fall within a random distribution with a mean of zero (0) and a variance of one (1), by using the following formulae: įirst, consider two random variables, and, both of which are independent random variables on. One method for generating a Gaussian distribution with a mean of zero (0) and a variance of one (1) is the Box-Muller method as described in. MATLAB comes with a tool, normpdf, which allows us to generate a Gaussian/normal distribution easily enough, but we’d prefer to do everything from the ground-up so that we can learn more from this. So, for each pixel in the original source image, the output after the addition of noise will be roughly equal to the sum of the original pixel value, and a random variable in the neighborhood of the mean value of the noise being added.īefore we continue, we should ask ourselves this: how can we generate Gaussian noise to apply to an image. Now, with respect to image processing, the addition of Gaussian noise essentially means that the input image has been altered due to the addition of a Gaussian random variable with mean and variances, where is the square-root of the variance, also known as the standard deviation. The curve’s peak is centered at the mean (-10), while the increased variance has caused the curve to spread-out more along the x-axis. Gaussian distribution (mean = -10, variance = 5)

Krita gaussian noise reduction