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Measurements of wave heights in marginal ice zones are limited to very few in situ data. Here we revisit the linear and quasilinear theories of Synthetic Aperture Radar imaging of waves in the particular case of waves in sea ice. Instead of only working with spectra, we have developed an iterative nonlinear algorithm to estimate phase-resolved deterministic maps of wave-induced orbital velocities, from which elevation spectra can be derived. Application of this algorithm to Sentinel 1A wave mode images in the Southern Ocean shows that it produces reasonable results for swells in all directions except when they propagate at a few degrees off the range direction. The estimate of wave parameters is expected to work best when the shortest wave components, those which cause a pixel displacement of the order of the dominant wavelength in azimuth, can be neglected. Otherwise short waves produce a blurring of the image, increasing exponentially with the azimuthal wavenumber and reducing the estimated wave amplitude. Given the expected spatial attenuation of waves in ice-covered regions, our deterministic method should apply beyond a few tens of kilometers in the ice, without any correction for short wave effects. In situ data collected around the ice edge as part of the 2015 SeaState DRI cruise in the Beaufort confirm the progressive image blurring caused by such short waves, and the apparent reduction in the wave modulation. When short waves propagate from the open ocean towards the ice, this blurring can produce an unrealistic apparent increase of wave height, from the open ocean up to a few tens of kilometers inside the ice. [ABSTRACT FROM AUTHOR]