I'm new the the mathhelpforums, so I want to start this post out with a big hello! I'm working on a math problem (for personal use) and I don't have anyone to turn to for help, so I figured I would look for help on this forum.
What I'm trying to do is reconstruct a vector field (as best I can) from projections of the field along lines passing through the field. Specifically, my lines carve out a 3D cone in the field, they all emerge from the same point. From what I've gathered thus far, it looks like the a solution to problem might lie the area of vector field tomography. The only trouble is, I haven't figured out how to apply any of the things I've found so far. Does anyone on this forum know anything about vector field reconstruction? If so, I would love to hear some suggestions or advice!
On the surface, it looks like the problem is of the form Ax=b. I know b and what I want is x, but the problem is that I don't know A. I've looked at some work on 3D cone beam doppler tomography and the method of approximate inverse, but like I said, I haven't figured out how to apply it, so I can't test it.