  Current high-resolution imaging techniques require an intact sample that
preserves spatial relationships. We here present a novel approach, "puzzle
imaging," that allows imaging a spatially scrambled sample. This technique
takes many spatially disordered samples, and then pieces them back together
using local properties embedded within the sample. We show that puzzle imaging
can efficiently produce high-resolution images using dimensionality reduction
algorithms. We demonstrate the theoretical capabilities of puzzle imaging in
three biological scenarios, showing that (1) relatively precise 3-dimensional
brain imaging is possible; (2) the physical structure of a neural network can
often be recovered based only on the neural connectivity matrix; and (3) a
chemical map could be reproduced using bacteria with chemosensitive DNA and
conjugative transfer. The ability to reconstruct scrambled images promises to
enable imaging based on DNA sequencing of homogenized tissue samples.
