Chirp signal correlation in the wavelet domain

From classical image processing it is known that correlations can be computed either in the spatial domain or in the Fourier transform domain. The advent of efficient wavelet transform techniques prompted the authors to investigate the chances for such computations using wavelet transformed data. The authors selected complex chirp signals as a typical example of signal correlation in the field of SAR data processing. Basic figures of merit are the fall-off of the correlation peak, the magnitude of secondary maxima, and the shift invariance of the selected correlation technique. Further, the correlation performance of noisy and degraded signals is of prime importance. In comparison with conventional chirp correlations in the Fourier domain, a straightforward signal correlation of wavelet transformed data leads to typical shift-variance and wavelet selection problems. The number of decomposition levels has to be optimized, too. All these problems can be tackled by re-arranging the wavelet transform coefficients and by using a nondecimating wavelet transform. On the other hand, the authors have to constrain the magnitude of secondary correlation maxima. The performance of various alternatives will be demonstrated by comparing algorithmic approaches, their implementation, and their figures of merit