John von Neumann’s Space-Frequency Orthogonal Transforms

Dan Stefanoiu and Janetta Culita ()
Additional contact information
Dan Stefanoiu: Faculty of Automatic Control and Computers, National University of Science and Technology POLITEHNICA Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania
Janetta Culita: Faculty of Automatic Control and Computers, National University of Science and Technology POLITEHNICA Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania

Mathematics, 2024, vol. 12, issue 5, 1-31

Abstract: Among the invertible orthogonal transforms employed to perform the analysis and synthesis of 2D signals (especially images), the ones defined by means of John von Neumann’s cardinal sinus are extremely interesting. Their definitions rely on transforms similar to those employed to process time-varying 1D signals. This article deals with the extension of John von Neumann’s transforms from 1D to 2D. The approach follows the manner in which the 2D Discrete Fourier Transform was obtained and has the great advantage of preserving the orthogonality property as well as the invertibility. As an important consequence, the numerical procedures to compute the direct and inverse John von Neumann’s 2D transforms can be designed to be efficient thanks to 1D corresponding algorithms. After describing the two numerical procedures, this article focuses on the analysis of their performance after running them on some real-life images. One black and white and one colored image were selected to prove the transforms’ effectiveness. The results show that the 2D John von Neumann’s Transforms are good competitors for other orthogonal transforms in terms of compression intrinsic capacity and image recovery.

Keywords: orthogonal transforms; time/space-frequency dictionary; windowed Fourier Transforms; analysis and synthesis of images (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/5/767/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/5/767/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:5:p:767-:d:1351076

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().