Improved Algorithms for Matrix Recovery from Rank-One Projections
This addresses matrix recovery challenges in applications like signal processing, but appears incremental as it builds on existing low-rank approximation techniques.
The paper tackles the problem of estimating a low-rank matrix from noisy rank-one projections by proposing two fast, non-convex algorithms, achieving linear convergence and sample complexity independent of the condition number.
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence and that their sample complexity is independent of the condition number of the unknown true low-rank matrix. By leveraging recent advances in low-rank matrix approximation techniques, we show that our algorithms achieve computational speed-ups over existing methods. Finally, we complement our theory with some numerical experiments.