S. Mann, S. Haykin

Abstract

We propose a novel transform, an expansion of an arbitrary function onto a basis of multi­scale chirps (swept frequency wave packets). We apply this new transform to a practical problem in marine radar: the detection of floating objects by their "acceleration signature" (the "chirpyness" of their radar backscatter), and obtain results far better than those previously obtained by other current Doppler radar methods. Each of the chirplets essentially models the underlying physics of motion of a floating object. Because it so closely captures the essence of the physical phenomena, the transform is near optimal for the problem of detecting floating objects. Besides applying it to our radar image processing interests, we also found the transform provided a very good analysis of actual sampled sounds, such as bird chirps and police sirens, which have a chirplike nonstationarity, as well as Doppler sounds from people entering a room, and from swimmers amid sea clutter. For the development, we first generalized Gabor's notion of expansion onto a basis of elementary "logons" (within the Weyl­Hiesenberg group) to the extent that our generalization included, as a special case, the wavelet transform (expansion in the affine group). We then extended that generalization further to include what we call "chirplets". We have coined the term "chirplet transform" to denote this overall generalization. Thus the Weyl­Hiesenberg and affine groups are both special cases of our chirplet transform, with the "chipyness" (Doppler acceleration) set to zero. We lay the foundation for future work which will bring together the theories of mixture distributions (Expectation Maximization) and our "Generalized Logon Transform