Question

The standard deviation ‘σ’ at any point in image averaging: σḡ(x, y) = 1/√K σɳ(x, y), where ḡ(x, y) is the average image formed by averaging K different noisy images and ɳ(x, y) is the noise added to an original image f(x, y). What is the relation between K and the variability of the pixel values at each location (x, y)?

(a) Increase in K, decreases the noise of pixel values

(b) Increase in K, increases the noise of pixel values

(c) Decrease in K, decreases the noise of pixel values

(d) Decrease in K, increases the noise of pixel values

The question was asked in a national level competition.

My question comes from Enhancement using Arithmetic Operations in section Image Enhancement of Digital Image Processing

Answer 1

The correct option is (a) Increase in K, decreases the noise of pixel values

To explain I would say: As K increases, E {ḡ(x, y)} the expected value approaches f(x, y) the original image, i.e. decreasing the noise component.