Designing and using prior data in Ankylography: Recovering a 3D object from a single diffraction intensity pattern

It was recently demonstrated [1] that a 3D object can be reconstructed from a single measurement of 2D diffraction intensity pattern by the technique called “Ankylography”. However, “...rather than sparking a revoution in imaging, the idea has raised objections from researchers who say that it amounts to pulling a threedimensional rabbit out of a two-dimensional hat” [2] (see also [3, 4]). To the best of our knowledge, the common consensus is that current reconstruction methods are not suitable for objects larger than about 15 15 15 × × voxels (volume elements). This limitation stems from the fact that for an object of size n n n × × voxels the number of measurements is proportional to 2 n ; hence, the ratio between the number of measurements and the number of unknowns is 1/ n , which makes the reconstruction problematic for large n . Furthermore, the current reconstruction methods do not easily allow introduction of prior information which can aid reconstruction. Here, we present a new approach enabling the reconstruction of objects with many more details, at very high accuracy.