John von Neumann’s Space-Frequency Orthogonal Transforms
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-varyin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/767 |
| _version_ | 1797264170529325056 |
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| author | Dan Stefanoiu Janetta Culita |
| author_facet | Dan Stefanoiu Janetta Culita |
| author_sort | Dan Stefanoiu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T00:24:39Z |
| format | Article |
| id | doaj.art-a683b5fcab9c43878335a7ad1d0555f9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-25T00:24:39Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a683b5fcab9c43878335a7ad1d0555f92024-03-12T16:50:16ZengMDPI AGMathematics2227-73902024-03-0112576710.3390/math12050767John von Neumann’s Space-Frequency Orthogonal TransformsDan Stefanoiu0Janetta Culita1Faculty of Automatic Control and Computers, National University of Science and Technology POLITEHNICA Bucharest, 313 Splaiul Independentei, 060042 Bucharest, RomaniaFaculty of Automatic Control and Computers, National University of Science and Technology POLITEHNICA Bucharest, 313 Splaiul Independentei, 060042 Bucharest, RomaniaAmong 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.https://www.mdpi.com/2227-7390/12/5/767orthogonal transformstime/space-frequency dictionarywindowed Fourier Transformsanalysis and synthesis of images |
| spellingShingle | Dan Stefanoiu Janetta Culita John von Neumann’s Space-Frequency Orthogonal Transforms Mathematics orthogonal transforms time/space-frequency dictionary windowed Fourier Transforms analysis and synthesis of images |
| title | John von Neumann’s Space-Frequency Orthogonal Transforms |
| title_full | John von Neumann’s Space-Frequency Orthogonal Transforms |
| title_fullStr | John von Neumann’s Space-Frequency Orthogonal Transforms |
| title_full_unstemmed | John von Neumann’s Space-Frequency Orthogonal Transforms |
| title_short | John von Neumann’s Space-Frequency Orthogonal Transforms |
| title_sort | john von neumann s space frequency orthogonal transforms |
| topic | orthogonal transforms time/space-frequency dictionary windowed Fourier Transforms analysis and synthesis of images |
| url | https://www.mdpi.com/2227-7390/12/5/767 |
| work_keys_str_mv | AT danstefanoiu johnvonneumannsspacefrequencyorthogonaltransforms AT janettaculita johnvonneumannsspacefrequencyorthogonaltransforms |