Further work

Derivation of a warp function is fundamentally a non-linear process, and I am never going to be able to escape that fact. However, there are tractable and non-tractable non-linear problems that we have some experience with. By formulating the problem of finding a warp function in the framework of geophysical estimation theory, I have opened up many possible avenues of exploration.

A big problem is the presence of secondary maxima that confuse the picking operation; ideally we would like to pick from functions with unique maxima. We may be able to achieve this goal by imposing a minimum-entropy condition Thorson (1984) on the shaping filter regularization (model-space residual). In practice, however, this may have convergence problems, and we may be better off with an L₁ norm on the model-space residual Nichols (1994), or even the Huber norm Guitton (2000).