ABSTRACT

Wiener filtering is linear, time invariant, mean square estimation of the unknown. The normal equations of linear algebra are linear, mean square estimation of the data. The Wiener filter is defined in terms of the power spectral density functions. Although it operates directly on the process, it is defined in terms of the squared properties of the process. The Wiener filter model assumes additive noise where the signal and the noise are jointly stationary. Although the assumption of additive noise and of stationarity is not strictly accurate, this model is reasonable for many planar radiologic imaging applications. The Wiener filter is equal to the ratio of the mutual power spectral density of the signal and the data to the power spectral density of the data. If the signal and the noise are uncorrelated, then the Wiener filter is the ratio of the signal to the signal plus the noise power spectral density functions.