This work proposes the first set of simple, practically useful, and provable algorithms for two inter-related problems. (i) The first is low-rank matrix recovery from magnitude-only (phaseless) linear projections of each of its columns. This finds important applications in phaseless dynamic imaging, e.g., Fourier Ptychographic imaging of live biological specimens. Our guarantee shows that, in the regime of small ranks, the sample complexity required is only a little larger than the order-optimal one, and much smaller than what standard (unstructured) phase retrieval methods need. %Moreover our algorithm is fast and memory-efficient if only the minimum required number of measurements is used (ii) The second problem we study is a dynamic extension of the above: it allows the low-dimensional subspace from which each image/signal (each column of the low-rank matrix) is generated to change with time. We introduce a simple algorithm that is provably correct as long as the subspace changes are piecewise constant.
Seyedehsara Nayer (Iowa State University)
Praneeth Narayanamurthy (Iowa State University)
Namrata Vaswani (Iowa State University)
Related Events (a corresponding poster, oral, or spotlight)
2019 Oral: Phaseless PCA: Low-Rank Matrix Recovery from Column-wise Phaseless Measurements »
Tue Jun 11th 10:10 -- 10:15 PM Room Room 102