Content:
Robust principal component pursuit (RPCP) refers to a decomposition of a data matrix into a low-rank component and a sparse component. In this work, instead of invoking a convex-relaxation model based on the nuclear norm and the `1 -norm as is typically done in this context, RPCP is solved by considering a least-squares problem subject to rank and cardinality constraints. An inexact alternating minimization scheme, with guaranteed global convergence, is employed to solve the resulting constrained minimization problem. In particular, the low-rank matrix subproblem is resolved inexactly by a tailored Riemannian optimization technique, which favorably avoids singular value decompositions in full dimen- sion. For the overall method, a corresponding q-linear convergence theory is established. The numerical experiments show that the newly proposed method compares competitively with a popular convex-relaxation based approach.
Content:
Peer Reviewed
Note:
The final publication is available at Springer via http://dx.doi.org/10.1007/s10851-014-0527-y
In:
Journal of Mathematical Imaging and Vision, : Springer, 2015, 51,2014,3, Seiten 361-377
Language:
English
URN:
urn:nbn:de:kobv:11-100246499
URL:
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