Tomography is a classic inverse problem in which multiple density pro jections of an ob ject are processed to infer some approximation of the original. We consider the highly sparse inverse problem of single angle pro jection, but seek to reduce the ambiguity through multiple time observations in a dynamic system of known or partially known dynamics. In this work we solve the planar problem by optimization techniques based on a gradient-free multi-directional search algorithm to minimize our nonlinear functional. We demonstrate convincingly successful numerical examples to support our relatively simple technique.