# Explain about image averaging process.

### Image Averaging:

Consider a noisy image g(x, y) formed by the addition of noise h(x, y) to an original image f(x,y); that is,

where the assumption is that at every pair of coordinates (x, y) the noise is uncorrelated and has zero average value.The objective of the following procedure is to reduce the noise content by adding a set of noisy images, {gi (x, y)}. If the noise satisfies the constraints just stated, it can be

shown that if an image               is formed by averaging K different noisy images,

Then it follows that

and

Where     is the expected value of     and   and              are the variances of and η, all at coordinates (x, y). The standard deviation at any point in the average image is

As K increases, the above equations indicate that the variability  (noise) of the pixel values at

each   location   (x,   y)   decreases.Because                                           this means that approaches f(x, y) as the number of noisy images used in the averaging process increases. In practice, the images gi(x, y) must be registered (aligned) in order to avoid the introduction of blurring and other artifacts in the output image.

Oct 15, 2021

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