Wavelets for $L^2(B(0,1))$ using Zernike polynomials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908461381451776 |
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| author | Datta, Somantika Datta, Kanti B. |
| author_facet | Datta, Somantika Datta, Kanti B. |
| contents | A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of $L^2(B(0,1)).$ This naturally leads to a multiresolution analysis of $L^2(B(0,1)).$ Previously, other authors have dealt with the one dimensional case, and used orthogonal polynomials of a single variable to construct time localized bases for polynomial subspaces of an $L^2$-space with arbitrary weight. Due to the nature of Zernike polynomials, the wavelet construction given here is well-suited for the analysis of two-dimensional signals defined on circular domains. This is shown by some experimental results done on corneal data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wavelets for $L^2(B(0,1))$ using Zernike polynomials Datta, Somantika Datta, Kanti B. Functional Analysis A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of $L^2(B(0,1)).$ This naturally leads to a multiresolution analysis of $L^2(B(0,1)).$ Previously, other authors have dealt with the one dimensional case, and used orthogonal polynomials of a single variable to construct time localized bases for polynomial subspaces of an $L^2$-space with arbitrary weight. Due to the nature of Zernike polynomials, the wavelet construction given here is well-suited for the analysis of two-dimensional signals defined on circular domains. This is shown by some experimental results done on corneal data. |
| title | Wavelets for $L^2(B(0,1))$ using Zernike polynomials |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2405.08129 |