Nov. 22, 2012
The use of ray-theoretical approximations allows us to image long-wavelength structure. To increase resolution, however, we cannot escape using the wave equation. Modeling the waveforms themselves is highly nonlinear, but the nonlinearity of the problem can be kept under control by using secondary observables such as delays of time- and frequency windowed waveforms.
The resulting problem is a giant linear inverse problem that is at the same time under- and overdetermined. Regularization techniques include total variation minimization and compressed sensing.
The estimation of accuracy and resolution of a solution poses a number of unsolved questions of mathematical nature.
Guust Nolet (GEOAZUR)