Dense target signal processing

The problem of determining the density of targets at every range and velocity is addressed. These targets consist of a dense group of reflecting objects moving with different velocities and at different ranges. The problem of how to choose the outgoing signals and process the echoes of those signals from the targets to determine the density function is discussed. The problem is a classical inverse problem. The objective is to reconstruct a function of two variables (range and velocity) from limited information. Two schemes are given. The first of these methods modifies the method of J.R. Klauder et al. (1960) to the case of signals with a large range of frequency components (wideband signals). The second is an improvement on the first that uses a formula of I. Khalil (1974) from affine group theory. Numerical solutions support the conclusions. The method has applications in echocardiography, radar, sonar and fluid flow measurement