Hierarchical calculation of cross-correlation functions and its application to SAR range compression

This paper proposes a method that calculates the approximate cross‐correlation between two discrete sequences with high speed. The method is evaluated by applying the idea to range compression in the SAR image reconstruction process. When the sequences are very long, tremendous computation time is required, even if the cross‐correlation function is calculated through the frequency domain. This is a problem when real‐time processing is required. In such a case, however, it is often more important to determine the approximate value with high speed than to determine precisely the value of the cross‐correlation function. From this viewpoint, this paper proposes a method in which the wavelet transform is applied to the two sequences, and the correlation function for the obtained short sequences is defined as an approximation to the original correlation function. By forming a hierarchy of wavelet functions, a hierarchy of approximate values is formed according to their accuracy. It is also possible, by successively improving the accuracy starting from a coarse approximation, to finally obtain the accurate value. The algorithm for such an idea is presented. Then, by applying the idea to the SAR range compression, the proposed method is experimentally evaluated. © 2000 Scripta Technica, Electron Comm Jpn Pt 1, 83(6): 10–20, 2000