  This work is concerned with the estimation of radial velocities of sea
surface elevations. The data, is a noisy along-track interferometric synthetic
aperture radar (AT-INSAR) image. We assume the Velocity Bunching Model. This
model relates the complex AT-INSAR image at a point in the image plane, with
the radial velocity of a scatterer point in the sea surface. The relation is by
means of a nonlinear integral operator mapping radial velocities into AT-INSAR
images. Consequently, the estimation of radial velocities, amounts to the
solution of nonlinear integral equations. Our proposal is to solve the latter
by Newton's methods on function spaces, the optimize then discretize approach.
We show that this continuous version is accurate, and faster than the classical
discretize then optimize version. Also a physical comparison is carried out
with the interferometric velocities.
