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Images obtained by airborne along‐track interferometric synthetic aperture radar (AT‐INSAR), provide tools to obtain ocean surface properties, such as the radial velocities of sea surface elevations. The estimation of these radial velocities from AT‐INSAR images is the interest of this work. We assume the Velocity Bunching Model relating 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. Consequently, the estimation of radial velocities amounts to the solution of nonlinear and oscillatory integral equations. Our proposal is to solve the latter by Newton's methods on Hilbert function spaces, the so‐called optimize then discretize approach. The effectiveness is illustrated by means of numerical simulations evaluating the reconstruction of the radial velocities and the AT‐INSAR image. We show that this continuous version is accurate, and faster than the classical discretize then optimize version. A physical comparison is also carried out with the interferometric velocities.

Ocean Surface Radial Velocity Imaging in the AT‐INSAR Velocity Bunching Model: A Functional Approach