Detection of nonlinearity in sea surface SAR imaging process using bispectrum method estimation

Higher order moments have been, for the last decade, an important field of interest, but generally limited to one dimensional signal cases. We introduce in this paper a 2D bispectrum to detect nonlinearity in the SAR image mapping process, by using the bicoherency of a 2D signal which is theoretically flat over all frequencies, if the process is linear. Two bicoherency estimators are developed, the first one using a direct method for bispectral estimation and a periodogram for the spectral estimator, and the second one based on an indirect method and correlogram. In order to validate our nonlinearity detection method, we have tested it first on two simulated images, a linear one and a nonlinear one, and then on two SAR images, one seeming to be nonlinear. Conclusions are drawn by comparing the SAR image and the simulated image bicoherencies