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Bilinear Parameterization for Non-Separable Singular Value Penalties

Örnhag, Marcus Valtonen LU ; Iglesias, José Pedro and Olsson, Carl LU (2021) 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021 In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition p.3896-3905
Abstract

Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from... (More)

Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from faster convergence. The bilinear framework is compatible with a large family of regularizers, and we demonstrate the benefits of our approach on real datasets for rigid and non-rigid structure from motion. The qualitative difference in reconstructions show that many popular non-convex objectives enjoy an advantage in transitioning to the proposed framework.

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author
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type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
series title
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
pages
10 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
conference location
Virtual, Online, United States
conference dates
2021-06-19 - 2021-06-25
external identifiers
  • scopus:85123192020
ISSN
1063-6919
ISBN
9781665445092
DOI
10.1109/CVPR46437.2021.00389
language
English
LU publication?
yes
id
9a5dc39f-ed92-499d-acb4-f5e7c782b802
date added to LUP
2022-03-24 15:19:46
date last changed
2022-05-02 18:15:07
@inproceedings{9a5dc39f-ed92-499d-acb4-f5e7c782b802,
  abstract     = {{<p>Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from faster convergence. The bilinear framework is compatible with a large family of regularizers, and we demonstrate the benefits of our approach on real datasets for rigid and non-rigid structure from motion. The qualitative difference in reconstructions show that many popular non-convex objectives enjoy an advantage in transitioning to the proposed framework.</p>}},
  author       = {{Örnhag, Marcus Valtonen and Iglesias, José Pedro and Olsson, Carl}},
  booktitle    = {{Proceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021}},
  isbn         = {{9781665445092}},
  issn         = {{1063-6919}},
  language     = {{eng}},
  pages        = {{3896--3905}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition}},
  title        = {{Bilinear Parameterization for Non-Separable Singular Value Penalties}},
  url          = {{http://dx.doi.org/10.1109/CVPR46437.2021.00389}},
  doi          = {{10.1109/CVPR46437.2021.00389}},
  year         = {{2021}},
}