Ultra Wide Band ISAR imaging by Laguerre Gauss tomographic reconstruction

When the angle covered by the target as seen by the sensor is sufficiently narrow, the ISAR imaging technique can be viewed as the tomographic reconstruction process of a synthetic image, which maps on space coordinates the energy backscattered from the target along different observation lines. As an alternative to the Fourier slice based techniques, in this paper a map reconstruction method from its two-dimensional (2-D) Laguerre Gauss (LG) expansion is presented. The LG expansion was already used for efficiently analyzing the orientation and the cross profile of linear patterns in images within a Maximum Likelihood approach. In particular, LG basis functions and expansion coefficients rotate by a simple phase shift, proportional to the rotation angle and the circular harmonic order. In addition, the LG expansion is linearly related to the 2-D Hermite Gauss (2-D HG) expansion, which allows for efficient numerical realizations and a compact model of the returns of Ultra Wide Band (UWB) waveforms, naturally suited for this high resolution scheme. The LG or the 2-D HG truncated expansion of the map is finally computed by the linear Least Squares interpolation of a set of matched filter outputs and used for reconstructing the backscattering map. Several system aspects of the LG ISAR method are discussed and computer experiments with tight concentrations of point scatterers illuminated by UWB pulse trains are presented.