Chi, Y; Eldar, YC; Calderbank, R, *PETRELS: Parallel Subspace Estimation and Tracking by Recursive Least Squares From Partial Observations*,
Ieee Transactions on Signal Processing, vol. 61 no. 23
(December, 2013),
pp. 5947-5959, Institute of Electrical and Electronics Engineers (IEEE) [1207.6353v2], [doi] .
**Abstract:**

*Many real world data sets exhibit an embedding of low-dimensional structure
in a high-dimensional manifold. Examples include images, videos and internet
traffic data. It is of great significance to reduce the storage requirements
and computational complexity when the data dimension is high. Therefore we
consider the problem of reconstructing a data stream from a small subset of its
entries, where the data is assumed to lie in a low-dimensional linear subspace,
possibly corrupted by noise. We further consider tracking the change of the
underlying subspace, which can be applied to applications such as video
denoising, network monitoring and anomaly detection. Our problem can be viewed
as a sequential low-rank matrix completion problem in which the subspace is
learned in an on-line fashion. The proposed algorithm, dubbed Parallel
Estimation and Tracking by REcursive Least Squares (PETRELS), first identifies
the underlying low-dimensional subspace via a recursive procedure for each row
of the subspace matrix in parallel with discounting for previous observations,
and then reconstructs the missing entries via least-squares estimation if
required. Numerical examples are provided for direction-of-arrival estimation
and matrix completion, comparing PETRELS with state of the art batch
algorithms.*