Coherence estimation for SAR imagery

In dual- or multiple-channel synthetic aperture radar (SAR) imaging modes, cross-channel correlation is a potential source of information. The sample coherence magnitude is calculated over a moving window to generate a coherence magnitude map. High-resolution coherence maps may be useful to discriminate fine structures. Coarser resolution is needed for a more accurate estimation of the coherence magnitude. In this study, the accuracy of coherence estimation is investigated as a function of the coherence map resolution. It is shown that the space-averaged coherence magnitude is biased toward higher values. The accuracy of the coherence magnitude estimate obtained is a function of the number of pixels averaged and the number of independent samples per pixel (i.e., the coherence map resolution). A method is proposed to remove the bias from the space-averaged sample coherence magnitude. Coherence magnitude estimation from complex (magnitude and phase) coherence maps is also considered. It is established that the magnitude of the averaged sample coherence estimate is slightly biased for high-resolution coherence maps and that the bias reduces with coarser resolution. Finally, coherence estimation for nonstationary targets is discussed. It is shown that the averaged sample coherence obtained from complex coherence maps or coherence magnitude maps is suitable for estimation of nonstationary coherence. The averaged sample (complex) coherence permits the calculation of an unbiased coherence estimate, provided that the original signals can be assumed to be locally stationary over a sufficiently coarse resolution cell.