PhaST: Model-free Phaseless Subspace Tracking

Seyedehsara Nayer, Namrata Vaswani

Abstract: Phaseless subspace tracking is the problem of recovering a time sequence of discrete signals from magnitude-only measurements of their linear projections, when the true signal lies in a low-dimensional subspace that can change with time. A typical assumption used in a lot of work is that the subspace changes gradually over time. We define this as (i) the maximum principal angle between the old and new subspaces is not too large (less than 90 degrees) or the number directions that changes is few or both; and (ii) the delay between subspace change times is large enough. This paper presents a novel algorithm, that we call PhaST, for model-free, mini- batch and fast Phaseless Subspace Tracking. We show via experiments that PhaST is significantly faster, and significantly more memory-efficient, than an existing algorithm for low- rank phase retrieval (which can be interpreted as a batch version of phaseless subspace tracking that does not assume anything about subspace changes). When fewer measurements are available, it also has significantly better recovery performance than both LRPR and single signal phase retrieval methods when its structural assumptions are valid.