Abstract
We revisit the problem of recovering a low-rank positive semidefinite matrix
from rank-one projections using tools from optimal transport. More
specifically, we show that a variational formulation of this problem is
equivalent to computing a Wasserstein barycenter. In turn, this new perspective
enables the development of new geometric first-order methods with strong
convergence guarantees in Bures-Wasserstein distance. Experiments on simulated
data demonstrate the advantages of our new methodology over existing methods.