On the theory of function-valued mappings and its application to the processing of hyperspectral images

Daniel Otero, Davide La Torre, Oleg Michailovich, Edward R. Vrscay

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)185-196
Number of pages12
JournalSignal Processing
Volume134
DOIs
Publication statusPublished - May 1 2017

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Processing
Fractals
Image processing
Imaging techniques

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 journalArticle

Otero, Daniel ; La Torre, Davide ; Michailovich, Oleg ; Vrscay, Edward R. / On the theory of function-valued mappings and its application to the processing of hyperspectral images. In: Signal Processing. 2017 ; Vol. 134. pp. 185-196.
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