Signal-to-noise ratio considerations in modified matched spatial filters

General expressions are derived for the degradation in the signal-to-noise ratio (SNR) as a function of rotation and scale distortions for modified matched spatial filters. These are numerically evaluated for image classes with Gaussian- and exponential-shaped autocorrelation functions to demonstrate the effects of training set size, input noise level, and image space–bandwidth product (SBWP) on the resulting SNR. The SNR for distorted input images is shown to improve, whereas the SNR for undistorted inputs degrades, as the number of training set images is increased. If the number of training set images is increased beyond a certain point, the SNR becomes constant for any input distortion. This SNR and the number of training set images required to attain it increase with the SBWP. The optimum training set image SBWP for a fixed training set size is also determined.