[kxyvr]

True. That said, I'll also mention that tomography is a very rich, interesting field that's still open to new innovations. I work in the area and unfortunately needed to pass on a muon tomography contract some years ago. By the way, you may know this, but the following is for the broader audience.

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If anyone is interested, the book Parameter Estimation and Inverse Problems by Aster, Borchers, and Thurber give an easy introduction to simple tomography problems in their book. Example 1.12 in their second edition has a very basic setup. More broadly, tomography intersects with an area of study called PDE constrained optimization. Commonly, tomography problems are setup as a large optimization problem where the difference between experimental data and the output of a simulation are minimized. Generally, the simulation is parameterized on the material properties of whatever is under study and are the optimization variables. The idea is that whatever material property that produces a simulation that matches the experimental data is probably what's there. This material property could be something simple like density or something more complicated like a full elasticity tensor.

What makes this difficult, is that most good simulations come from a system of differential equations, which are infinite dimensional and not suitable for running directly in an optimization algorithm. As such, care must be taken into discretizing the system carefully, so that the optimization tool produces something reasonable and physical. Words you'll see are things like discretize-then-optimize or optimize-then-discretize. Generally speaking, the whole system works very, very poorly if one just takes an existing simulator and slaps an optimizer on it. Care must be taken to do it right.

As far as the optimizer, the scale is pretty huge. It's common to see hundreds of millions of variables if not more. In addition, the models normally need to be bounded, so there are inequalities that must be respected. For example, if something like a density isn't bounded to be positive (which is physical), then the simulator itself may diverge (a simulator here may be something like a Runge-Kutta method.)

Anyway, it's a big combination of numerical PDEs, optimization, HPC, and other tools just to get a chance to run something. Something like the detector in the article is very cool because it may be a realistic way to get data to test against for super cheap.