Abstract: Suppose an asteroid is so far away that only a single pixel of light can be measured at any time. The measurement is proportional to the area of the profile of the asteroid in the viewing direction - that is, the area of its orthogonal projection onto a plane orthogonal to this direction. Once several such measurements have been taken, they must be processed somehow to produce an image of the asteroid. How can this be done? The talk will describe joint work with an electrical engineer, Peyman Milanfar of UC Santa Cruz. We have designed algorithms for this purpose, and with the help of a student, Chris Street, these have been implemented. The talk will include demonstrations of the algorithms. These given reconstructions in three dimensions, and are supported by convergence proofs.