RESUMEN

The shape-from-shading (SFS) equation relating u(y,r), the unknown (angular) height of a surface, to I(y,r), the known synthetic aperture radar (SAR) intensity data from the surface, is I = \frac{u_r^2}{\sqrt{1+u_r^2+u_y^2}}, where y and r are axial and radial cylindrical coordinates. Unlike the more common eikonal SFS equation which relates surface height in Cartesian coordinates to optical/photographic intensity data, the above radar equation can be transformed into Hamilton--Jacobi Cauchy form: u_r+g(I,u_y)=0. We explore the case where I is a discontinuous function, which occurs commonly in radar data. By considering sequences of continuous intensity functions that converge to I, we obtain corresponding sequences of viscosity solutions. We prove that these sequences must converge. We also establish conditions that guarantee that these sequences converge to a common limit, which we define as the solution to the radar equation. Finally, we establish and demonstrate that when this common limit exists, monotone numerical schemes must converge to this solution as the mesh size decreases.