Digital filtering for optimization of signals submerged in noise
S. Y. Lee · NASA STI Repository (National Aeronautics and Space Administration) · 1969
Photographic noise reduces the amount of image information that can be recorded.This memorandum is concerned with the problem of deriving an optimum linear filter for performing a spatial filtering operation on inputs, where the input consists of signal plus white noise, which have been recorded in a digital array as intensity values.This problem essentially boils down to a two-dimensional generalization of tAe frequency-domain filtering of time series.It is well known from network theory that the one-dimensional Wiener-Hopf equation for optimum linear filters minimizes the mean-square error between input and the desired output, where the input and the desired output are in the form of distributions.Elias, Grey and Robinson show that the one-dimensional Wiener-Hopf equation can be generalized to the multidimensional cases.Therefore by using the two-dimensional Wiener-Hopf equation and assuming the desired output is a circular disc with uniform intensity,* optimum linear filters are derived for a given quantity indicative of signal to noise ratio. II. THE TWO-DIMENSIONAL WIENER-HOPE EQUATIONConsider Im (x, y) , I s (x, y) and In (x, y ) be the intensity distributions of the message, its signal and noise components respectively, and let ^MJM (x,y) , ^s,s (x,y) and 0 nIn (x,y) be their