Usually these type of inverse problems are severely ill-defined. There can be many 3D configurations that give the 2D images, and you need to use some knowledge

Usually these type of inverse problems are severely ill-defined. There can be many 3D configurations that give the 2D images, and you need to use some knowledge of the world (or some regularization) to select which one is the most plausible. A typical application is when they measure brain signals at the surface of the brain and then try to reconstruct what happens inside. Have people thought of using genetic algorithms and other stochastic methods ? Probably yes.