HINTS

Naturally, if we are given specific information about the operator $\bold F$we can hope for better diagonal multiplers. Most of the practical problems I am familiar with are similar to the Radon transform except that straight lines in the Radon transform become various hyperbolas and hyperboloids.

The building blocks, as you see from the Symes guess and our follow-on guesses, include using the data vector $\bold d$.We may also use vectors of ones and vectors of random numbers in both data space and model space. We can take spatial derivatives in the geophysical model space $\bold m$,and likewise space and time derivatives in the data space $\bold d$.(The Radon transform special case shows that we might even need half-order derivatives.) We also have square roots of scalars and we have smoothing.