Linear interpolation between two images (a, and b):

∀ pixels:
   image <- (1 - alpha) * a + (alpha * b)

Uses

Change image brightness where A is a black image and B is the image being brightness adjusted.

Change image contrast where A is a constant grey (average luminance of B) and B is the image being contrast adjusted.

Sharpen an image where A is a blurred version and B is the image being sharpened.

Sometimes operations can be combined. A both blurred and desaturated version will have an effect.

Any convolution kernels can be used; convolve the image, interpolate between convolved and original.