Unconstrained inversion of waveheight spectra from SAR images

A procedure for inverting the nonlinear relationship between the waveheight spectrum and the SAR image spectrum is presented, and this procedure is evaluated using simulated data as well as actual ERS SAR data collected near Duck, NC. Results of this nonlinear inversion are compared with those obtained from a quasi-linear estimation procedure using simulated data, in order to illustrate the effects of nonlinearities in the imaging process. These effects include the well-known azimuth falloff effect as well as the generation of harmonics which appear in the background region of the spectrum. The nonlinear inversion technique is able to reproduce the input image spectrum to high accuracy, although the wave spectrum obtained by this procedure is not necessarily the same as the input wave spectrum. In general, the estimated wave spectrum is quite similar to the portion of the input wave spectrum within the SAR passband region, but none of the energy outside the passband is recovered. The background signals due to nonlinear effects can cause large errors in the quasi-linear estimation procedure because these signals appear in regions of the spectrum where the SAR modulation transfer function (mtf) is small. Results using actual SAR data also indicate that energy within the passband is recovered fairly accurately, although energy outside the passband is clearly lost. Estimates of the mean wavelength and direction for the in-band components become more accurate as the signal level increases, indicating that the errors are predominantly due to speckle noise rather than nonlinear imaging effects. Estimates of the significant waveheight are less influenced by speckle noise, and are accurate to within 0.14 m for this data set, if wind wave spectral peaks that are clearly outside the SAR passband are neglected.