Multiple scale correlation of chirp signal by discrete wavelet transform

Chirp signal, a finite duration pulse with linear frequency modulation (LFM) is the signal waveform widely used for coherent image formation. Coherent imagery is derived essentially as a 2-dimensional correlation of received, delayed chirp waveform with a 2-dimensional matched filter. There is wide and active research interest in analyzing coherent imagery at multiple scales for multiresolution speckle reduction, clutter separation from desired targets and other low level vision requirements such as multiple scale segmentation, etc. This paper attempts to address these requirements during the image formation process; i.e., obtaining multiple resolution imagery by signal correlation at multiple scales. We derive a shift and scale invariant DWT algorithm, which functions as the cornerstone for such multiple scale correlation. We also briefly discuss implications of this image formation algorithm with particular attention to speckle reduction.