Optimal Reduced Rank Modeling for General Noise Using Nullspace Estimation

The problem of optimal reconstruction of a lowrank matrix subject to additive noise of arbitrary noise color is addressed. We propose a non-iterative method based on modeling the nullspace of the data. The proposed technique is shown to yield statistically efficient estimates at sufficiently high Signal-to-Noise Ratio. Yet, the computational complexity is significantly reduced compared to existing methods. The empirical efficiency is verified using simulated data. In more difficult scenarios, the proposed NullSpace Estimator (NSE) can be used to initialize an iterative approach, and in the studied cases just one iteration of Alternating Least-Squares (ALS) was found enough.