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**Harvard**

Bylow, E., Olsson, C., Kahl, F. och Nilsson, M. (2016) *Minimizing the maximal rank*.

** BibTeX **

@conference{

Bylow2016,

author={Bylow, Erik and Olsson, Carl and Kahl, Fredrik and Nilsson, Mikael},

title={Minimizing the maximal rank},

booktitle={Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},

isbn={978-1-4673-8851-1},

pages={5887-5895},

abstract={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.},

year={2016},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 246238

A1 Bylow, Erik

A1 Olsson, Carl

A1 Kahl, Fredrik

A1 Nilsson, Mikael

T1 Minimizing the maximal rank

YR 2016

T2 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

SN 978-1-4673-8851-1

SP 5887

OP 5895

AB 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.

LA eng

DO 10.1109/CVPR.2016.634

LK http://dx.doi.org/10.1109/CVPR.2016.634

OL 30