Title :
PETRELS: Subspace estimation and tracking from partial observations
Author :
Chi, Yuejie ; Eldar, Yonina C. ; Calderbank, Robert
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA
Abstract :
We consider the problem of reconstructing a data stream from a small subset of its entries, where the data stream is assumed to lie in a low-dimensional linear subspace, possibly corrupted by noise. It is also important to track the change of underlying subspace for many applications. This problem can be viewed as a sequential low-rank matrix completion problem in which the subspace is learned in an online fashion. The proposed algorithm, called Parallel Estimation and Tracking by REcursive Least Squares (PETRELS), identifies the underlying low-dimensional subspace via a recursive procedure for each row of the subspace matrix in parallel, and then reconstructs the missing entries via least-squares estimation if required. PETRELS outperforms previous approaches by discounting observations in order to capture long-term behavior of the data stream and be able to adapt to it. Numerical examples are provided for direction-of-arrival estimation and matrix completion, comparing PETRELS with state of the art batch algorithms.
Keywords :
least squares approximations; matrix algebra; recursive estimation; signal reconstruction; PETRELS; data stream reconstruction; direction-of-arrival estimation; least-squares estimation; low-dimensional linear subspace; online fashion; parallel estimation and tracking by recursive least squares; partial observations; recursive procedure; sequential low-rank matrix completion problem; subspace estimation; subspace matrix completion; Direction of arrival estimation; Estimation; Least squares approximation; Noise; Signal processing algorithms; Vectors; matrix completion; recursive least squares; subspace estimation and tracking;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on
Conference_Location :
Kyoto
Print_ISBN :
978-1-4673-0045-2
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2012.6288621