Updating signal subspaces
Christian H Bischof, Gautam M. Shroff · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
We develop an algorithm for adaptively estimating the noise subspace of a data matrix as is required in signal processing applications employing the ''signal subspace'' approach. The noise subspace is estimated using a rank-revealing QR factorization instead of the more expensive singular value or eigenvalue decompositions. Using incremental condition estimation to monitor the smallest singular values of triangular matrices we can update the rank-revealing triangular factorization inexpensively when new rows are added and old rows are deleted. Experiments demonstrate that the new approach usually requires 0(n2) work to update an n x n matrix and accurately tracks the noise subspace.