Fast matrix inversion in compressive spectral imaging based on a tensorial representation
(2024) In Journal of Electronic Imaging 33(1).- Abstract
Snapshot spectral imaging enables the acquisition of hyperspectral images (HSI) employing specialized optical systems, such as the coded aperture snapshot spectral imager (CASSI). Specifically, the CASSI system performs spatiospectral codification of light obtaining two-dimensional projected measurements, and these measurements are then processed by computational algorithms to obtain the desired spectral images. However, because HSIs often have a high spatial or spectral resolution, the sensing matrix related to the acquisition protocol becomes very large, leading to a high computational storage cost and long computation times. In this work, we propose an algebraic framework for computing the relevant operations in a tensorial form... (More)
Snapshot spectral imaging enables the acquisition of hyperspectral images (HSI) employing specialized optical systems, such as the coded aperture snapshot spectral imager (CASSI). Specifically, the CASSI system performs spatiospectral codification of light obtaining two-dimensional projected measurements, and these measurements are then processed by computational algorithms to obtain the desired spectral images. However, because HSIs often have a high spatial or spectral resolution, the sensing matrix related to the acquisition protocol becomes very large, leading to a high computational storage cost and long computation times. In this work, we propose an algebraic framework for computing the relevant operations in a tensorial form based on the nature of the codification protocol. We then test our framework against some comparison methods based on linear algebra decomposition, factorization, or block-operations, demonstrating that the proposed method is between 3 and 20 times faster than the best-competing method. Moreover, the gain becomes larger when the matrices become bigger, corresponding to realistic HSI sizes for spectral imaging applications. In extreme cases, our method can still operate when the competing methods stall due to memory shortage.
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- author
- Carlsson, Marcus LU ; Martinez, Emmanuel ; Vargas, Edwin and Arguello, Henry
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- compressive sensing, hyperspectral imaging, linear algebra, non-linear operations
- in
- Journal of Electronic Imaging
- volume
- 33
- issue
- 1
- article number
- 013034
- publisher
- I S & T - SOC IMAGING SCIENCE TECHNOLOGY
- external identifiers
-
- scopus:85187182340
- ISSN
- 1017-9909
- DOI
- 10.1117/1.JEI.33.1.013034
- language
- English
- LU publication?
- yes
- id
- 1b7cb868-303a-4bd7-856f-8e412009d33f
- date added to LUP
- 2024-04-02 15:44:43
- date last changed
- 2024-04-02 15:45:21
@article{1b7cb868-303a-4bd7-856f-8e412009d33f,
abstract = {{<p>Snapshot spectral imaging enables the acquisition of hyperspectral images (HSI) employing specialized optical systems, such as the coded aperture snapshot spectral imager (CASSI). Specifically, the CASSI system performs spatiospectral codification of light obtaining two-dimensional projected measurements, and these measurements are then processed by computational algorithms to obtain the desired spectral images. However, because HSIs often have a high spatial or spectral resolution, the sensing matrix related to the acquisition protocol becomes very large, leading to a high computational storage cost and long computation times. In this work, we propose an algebraic framework for computing the relevant operations in a tensorial form based on the nature of the codification protocol. We then test our framework against some comparison methods based on linear algebra decomposition, factorization, or block-operations, demonstrating that the proposed method is between 3 and 20 times faster than the best-competing method. Moreover, the gain becomes larger when the matrices become bigger, corresponding to realistic HSI sizes for spectral imaging applications. In extreme cases, our method can still operate when the competing methods stall due to memory shortage.</p>}},
author = {{Carlsson, Marcus and Martinez, Emmanuel and Vargas, Edwin and Arguello, Henry}},
issn = {{1017-9909}},
keywords = {{compressive sensing; hyperspectral imaging; linear algebra; non-linear operations}},
language = {{eng}},
number = {{1}},
publisher = {{I S & T - SOC IMAGING SCIENCE TECHNOLOGY}},
series = {{Journal of Electronic Imaging}},
title = {{Fast matrix inversion in compressive spectral imaging based on a tensorial representation}},
url = {{http://dx.doi.org/10.1117/1.JEI.33.1.013034}},
doi = {{10.1117/1.JEI.33.1.013034}},
volume = {{33}},
year = {{2024}},
}