Minimizing the maximal rank
Paper i proceeding, 2016

In computer vision, many problems can be formulated as finding a low rank approximation of a given matrix. Ideally, if all elements of the measurement matrix are available, this is easily solved in the L2-norm using factorization. However, in practice this is rarely the case. Lately, this problem has been addressed using different approaches, one is to replace the rank term by the convex nuclear norm, another is to derive the convex envelope of the rank term plus a data term. In the latter case, matrices are divided into sub-matrices and the envelope is computed for each subblock individually. In this paper a new convex envelope is derived which takes all sub-matrices into account simultaneously. This leads to a simpler formulation, using only one parameter to control the trade-of between rank and data fit, for applications where one seeks low rank approximations of multiple matrices with the same rank. We show in this paper how our general framework can be used for manifold denoising of several images at once, as well as just denoising one image. Experimental comparisons show that our method achieves results similar to state-of-the-art approaches while being applicable for other problems such as linear shape model estimation.

Författare

Erik Bylow

Lunds universitet

Carl Olsson

Lunds universitet

Fredrik Kahl

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik, Digitala bildsystem och bildanalys

Mikael Nilsson

Lunds universitet

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

1063-6919 (ISSN)

Vol. 2016-January 5887-5895

Ämneskategorier

Data- och informationsvetenskap

Beräkningsmatematik

DOI

10.1109/CVPR.2016.634

ISBN

978-1-4673-8851-1