  Ultracold atoms in optical lattices form a clean quantum simulator platform
which can be utilized to examine topological phenomena and test exotic
topological materials. Here we propose an experimental scheme to measure the
Chern numbers of two-dimensional multiband topological insulators with bosonic
atoms. We show how to extract the topological invariants out of a sequence of
time-of-flight images by applying a phase retrieval algorithm to matter waves.
We illustrate advantages of using bosonic atoms as well as efficiency and
robustness of the method with two prominent examples: the Harper-Hofstadter
model with an arbitrary commensurate magnetic flux and the Haldane model on a
brick-wall lattice.
