Noise modelling in Image Processing

Design of filter is dependent of noise present in image. Most common noises are Gaussian noise, Exponential noise, Uniform noise, Salt and Pepper noise. Different types of filters are used to filter out the noise dependent of noise type. Noise in general is introduced because of motion and sensors.

Generally we all talk about additive noise and very very rarely the multiplicative noise because multiplicative noise are transformed to additive noise in logarithmic domain. So multiplicative noises are not discussed more in most of literatures. 

Mathematical Operations on Image

Averaging/Mean

Averaging is the methods of replacing pixel values which has effects of neighbours. Mean value is used to replace because mean value has minimum MSE. For the heat flow function, diffusion equation is satisfied with flow of pixel value. Blurring of a image is due to diffusion of gray values satisfying heat flow function.

Non local averaging is done to minimize the noise as the noise is proportional to square of number of neighbour similar windows or blocks of images. In general averaging introduces blurring.

Where as median filter, completely reduces noise with replacing noise added pixel with one of the values equal to pixel around it.

Derivatives are used to edge detection where as laplacian function is used to sharpen the image details. Laplacian function is the sum of second derivatives in both x and y directions.