Solution of biharmonic equations with application to radar imaging

In a radar imaging problem using broad-band, low-frequency waves, we encounter the problem of solving Poissonʹs equation over a very large rectangular grid, typically five thousand times thousand pixels. In addition, no information about boundary values is available. In order to select suitable solutions we solve the Poisson equation under the side condition that some criterion function, usually a Sobolev norm, should be minimized. Under appropriate smoothness assumptions this problem may be reformulated as a boundary value problem for the biharmonic equation. Numerical techniques are investigated for this problem. We also include the results of some numerical experiments