A log spectral approach to bidirectional deconvolution

CONCLUSIONS

It is too early to draw reliable conclusions about this theory. It arose a few weeks before the progress report deadline, and got coded a few days before. The coding (steepest descent) illuminated a bug in the initial theory regarding the constraint. A few test cases were successfully run, but we do not know how this method compares to Shen et al. (2011) and Fu et al. (2011).

The problem formulation itself is nonlinear and thereby susceptible to many minima, mostly bad ones. We don't know whether preconditioning applies in the usual way to this method. Perhaps some kind of tapering of $\Delta u_t$ is a means of directing the method towards a more appropriate optimum, but for now this is no more than speculation.