Computing the Lipschitz Constant Needed for Fast Scene Recovery from CASSI Measurements
Overgaard, Niels Christian LU and Holst, Anders LU
(2024)
18th European Conference on Computer Vision, ECCV 2024
In Lecture Notes in Computer Science
15120.
p.339-353
- Abstract
- The linear inverse problem associated with the standard model for hyperspectral image recovery from CASSI measurements is considered. This is formulated as the minimization of an objective function which is the sum of a total variation regularizer and a least squares loss function. Standard first-order iterative minimization algorithms, such as ISTA, FISTA and TwIST, require as input the value of the Lipschitz constant for the gradient of the loss function, or at least a good upper bound on this value, in order to select appropriate step lengths. For the loss term considered here, this Lipschitz constant equals the square of the largest singular value of the measurement map. In applications, this number is usually computed directly as the... (More)
- The linear inverse problem associated with the standard model for hyperspectral image recovery from CASSI measurements is considered. This is formulated as the minimization of an objective function which is the sum of a total variation regularizer and a least squares loss function. Standard first-order iterative minimization algorithms, such as ISTA, FISTA and TwIST, require as input the value of the Lipschitz constant for the gradient of the loss function, or at least a good upper bound on this value, in order to select appropriate step lengths. For the loss term considered here, this Lipschitz constant equals the square of the largest singular value of the measurement map. In applications, this number is usually computed directly as the largest eigenvalue of a huge square matrix. This can sometimes become a bottleneck in an otherwise optimized algorithm. In the present paper we effectively eliminate this bottleneck for CASSI reconstructions by showing how the Lipschitz constant can be calculated from a square matrix whose size is easily three orders of magnitudes smaller than in the direct approach.
(Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/fb44681b-a2f4-4515-83b8-ea849cfaed02
- author
- Overgaard, Niels Christian
LU
and Holst, Anders
LU
- organization
-
- Mathematical Imaging Group (research group)
- Engineering Mathematics (M.Sc.Eng.)
- Partial differential equations (research group)
- ELLIIT: the Linköping-Lund initiative on IT and mobile communication
- eSSENCE: The e-Science Collaboration
- LTH Profile Area: Engineering Health
- LTH Profile Area: AI and Digitalization
- Computer Vision and Machine Learning (research group)
- LU Profile Area: Natural and Artificial Cognition
- Algebra, Analysis and Dynamical Systems (research group)
- Mathematics (Faculty of Engineering)
- Harmonic Analysis and Applications (research group)
- publishing date
- 2024-10
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Computer Vision – ECCV 2024 : 18th European Conference, Milan, Italy, September 29–October 4, 2024, Proceedings, Part LXII - 18th European Conference, Milan, Italy, September 29–October 4, 2024, Proceedings, Part LXII
- series title
- Lecture Notes in Computer Science
- volume
- 15120
- pages
- 15 pages
- publisher
- Springer
- conference name
- 18th European Conference on Computer Vision, ECCV 2024
- conference location
- Milan, Italy
- conference dates
- 2024-09-29 - 2024-10-04
- external identifiers
-
- scopus:85208544942
- ISSN
- 0302-9743
- 1611-3349
- ISBN
- 978-3-031-73032-0
- 978-3-031-73033-7
- DOI
- 10.1007/978-3-031-73033-7_19
- language
- English
- LU publication?
- yes
- id
- fb44681b-a2f4-4515-83b8-ea849cfaed02
- date added to LUP
- 2025-01-10 13:16:25
- date last changed
- 2025-05-01 20:34:14
@inproceedings{fb44681b-a2f4-4515-83b8-ea849cfaed02,
abstract = {{The linear inverse problem associated with the standard model for hyperspectral image recovery from CASSI measurements is considered. This is formulated as the minimization of an objective function which is the sum of a total variation regularizer and a least squares loss function. Standard first-order iterative minimization algorithms, such as ISTA, FISTA and TwIST, require as input the value of the Lipschitz constant for the gradient of the loss function, or at least a good upper bound on this value, in order to select appropriate step lengths. For the loss term considered here, this Lipschitz constant equals the square of the largest singular value of the measurement map. In applications, this number is usually computed directly as the largest eigenvalue of a huge square matrix. This can sometimes become a bottleneck in an otherwise optimized algorithm. In the present paper we effectively eliminate this bottleneck for CASSI reconstructions by showing how the Lipschitz constant can be calculated from a square matrix whose size is easily three orders of magnitudes smaller than in the direct approach.<br/><br/>}},
author = {{Overgaard, Niels Christian and Holst, Anders}},
booktitle = {{Computer Vision – ECCV 2024 : 18th European Conference, Milan, Italy, September 29–October 4, 2024, Proceedings, Part LXII}},
isbn = {{978-3-031-73032-0}},
issn = {{0302-9743}},
language = {{eng}},
pages = {{339--353}},
publisher = {{Springer}},
series = {{Lecture Notes in Computer Science}},
title = {{Computing the Lipschitz Constant Needed for Fast Scene Recovery from CASSI Measurements}},
url = {{http://dx.doi.org/10.1007/978-3-031-73033-7_19}},
doi = {{10.1007/978-3-031-73033-7_19}},
volume = {{15120}},
year = {{2024}},
}