A wavelet detector for model-based imaging

This paper investigates the model-based aspects of the estimator correlator (EC) detector in the wavelet domain. Ideas from group theory are used to develop and describe underlying properties. By applying group representation theory to the detector development, insight into the optimal processing structure of the EC is gained. In the absence of a priori model information, the EC detector reduces to the wavelet domain or matched filter detector. With a priori information incorporated into the model, the EC becomes a weighted wavelet detector. Implementing the EC in the wavelet domain provides range-Doppler (wavelet) images at different stages of processing. This allows the opportunity to simultaneously exploit the vast body of knowledge of wavelets, scattering function theory, and range-Doppler processing techniques. Ambiguity function theory is used to evaluate performance capabilities of these wavelet-based detectors using various narrowband and wideband transmit signals. This paper shows that the weighted wavelet detector serves as a classifier as well by using the scattering function model as a basis for pattern recognition. An example of the effectiveness of the weighted wavelet detector with narrowband and wideband signals for a multi-highlight image model is presented and results are discussed.