Explicit solution of the eigenvalue integral with exponentially oscillating covariance function

摘要

The Karhunen-Loeve transform based on calculation of the eigenvalues and eigenfunctions of the Karhunen-Loeve integral equation is known to have certain properties which make it optimal for many signal detection and filtering applications. We propose an analytical solution of the equation for a practical case when the covariance function of a stationary process is exponentially oscillating. Computer simulation results using a real aerial image are provided and discussed.