Minimizing the Maximal Rank
(2016) 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016- 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 sub-block 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... (More)
- 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 sub-block 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.
(Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/a5fc8d48-430c-4110-aa31-4f0d7def5c15
- author
- Bylow, Erik LU ; Olsson, Carl LU ; Kahl, Fredrik LU and Nilsson, Mikael LU
- organization
- publishing date
- 2016
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- CVPR 2016, proceedings
- pages
- 9 pages
- conference name
- 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
- conference location
- Las Vegas, United States
- conference dates
- 2016-06-26 - 2016-07-01
- external identifiers
-
- scopus:84986260048
- language
- English
- LU publication?
- yes
- id
- a5fc8d48-430c-4110-aa31-4f0d7def5c15
- date added to LUP
- 2016-09-08 11:50:15
- date last changed
- 2022-01-30 05:57:30
@inproceedings{a5fc8d48-430c-4110-aa31-4f0d7def5c15,
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 sub-block 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.<br/>}},
author = {{Bylow, Erik and Olsson, Carl and Kahl, Fredrik and Nilsson, Mikael}},
booktitle = {{CVPR 2016, proceedings}},
language = {{eng}},
title = {{Minimizing the Maximal Rank}},
url = {{https://lup.lub.lu.se/search/files/11956514/multiblock.pdf}},
year = {{2016}},
}