Bilinear Parameterization for Non-Separable Singular Value Penalties

Marcus Valtonen Örnhag, José Pedro Iglesias, Carl Olsson

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

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 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.

Original languageEnglish
Title of host publicationProceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Pages3896-3905
Number of pages10
ISBN (Electronic)9781665445092
DOIs
Publication statusPublished - 2021
Event2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021 - Virtual, Online, United States
Duration: 2021 Jun 192021 Jun 25

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Conference

Conference2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
Country/TerritoryUnited States
CityVirtual, Online
Period2021/06/192021/06/25

Subject classification (UKÄ)

  • Computational Mathematics
  • Control Engineering

Fingerprint

Dive into the research topics of 'Bilinear Parameterization for Non-Separable Singular Value Penalties'. Together they form a unique fingerprint.

Cite this