Abstract
The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well.
| Original language | English |
|---|---|
| Pages (from-to) | 185-196 |
| Number of pages | 12 |
| Journal | Signal Processing |
| Volume | 134 |
| DOIs | |
| Publication status | Published - May 1 2017 |
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Keywords
- And fractal transform
- Banach spaces
- Fourier transform
- Function-valued functions
- Image processing
ASJC Scopus subject areas
- Control and Systems Engineering
- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
Cite this
On the theory of function-valued mappings and its application to the processing of hyperspectral images. / Otero, Daniel; La Torre, Davide; Michailovich, Oleg; Vrscay, Edward R.
In: Signal Processing, Vol. 134, 01.05.2017, p. 185-196.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the theory of function-valued mappings and its application to the processing of hyperspectral images
AU - Otero, Daniel
AU - La Torre, Davide
AU - Michailovich, Oleg
AU - Vrscay, Edward R.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well.
AB - The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well.
KW - And fractal transform
KW - Banach spaces
KW - Fourier transform
KW - Function-valued functions
KW - Image processing
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U2 - 10.1016/j.sigpro.2016.12.014
DO - 10.1016/j.sigpro.2016.12.014
M3 - Article
VL - 134
SP - 185
EP - 196
JO - Signal Processing
JF - Signal Processing
SN - 0165-1684
ER -