Summary: Subband coring for image noise reduction.
Edward H. Adelson
Internal Report, RCA David Sarnoff Research Center, Nov. 26 1986.
Let an image consisting of the array of pixels, E(x,y), be denoted E (the
boldface indicating that it is a discrete function over (x,y)). Likewise, let a
kernel with taps A(x,y) be denoted A. The image can be decomposed into a
set of N filtered subimages, S i, by convolution with the set of N kernels, Ai.
Let * indicate convolution; then the decomposition is:
E = S0+ . . . +S N-1
S i = E*Ai
We do not assume that the subimages have been decimated. Thus each
subimage has the same number of pixels as the original image, and the total
number of pixels in the decomposition is N times the number in the original
The kernels would normally be chosen to produce a decomposition into
a "useful" set of subimages. In the case of noise coring, this will usually mean
that the kernels are selective for orientation and scale, i.e. that they select out
limited patches in the spatial frequency domain. For example, we might
choose A1 to select for vertical energy, A2 to select for horizontal energy, and