Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915736025300992 |
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| author | Dizon, Neil D. Hogan, Jeffrey A. |
| author_facet | Dizon, Neil D. Hogan, Jeffrey A. |
| contents | This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard conditions of smoothness, compact support, and orthonormality. To solve the resulting feasibility problems, we employ a product space formulation of the Douglas-Rachford algorithm. This approach yields novel examples of nonseparable, multiresolution, compactly supported, smooth, and orthonormal quaternion-valued wavelets on the plane. Additionally, by introducing a symmetry-promoting constraint, we construct symmetric quaternion-valued scaling functions on the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12614 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach Dizon, Neil D. Hogan, Jeffrey A. Classical Analysis and ODEs 42C40, 42B99, 65T60, 47N10, 65K10 This paper presents a reformulation of the construction of nonseparable multiresolution quaternion-valued wavelets on the plane as a feasibility problem. The constraint sets in the feasibility problem are derived from the standard conditions of smoothness, compact support, and orthonormality. To solve the resulting feasibility problems, we employ a product space formulation of the Douglas-Rachford algorithm. This approach yields novel examples of nonseparable, multiresolution, compactly supported, smooth, and orthonormal quaternion-valued wavelets on the plane. Additionally, by introducing a symmetry-promoting constraint, we construct symmetric quaternion-valued scaling functions on the plane. |
| title | Quaternion-Valued Wavelets on the Plane: A Construction via the Douglas-Rachford Approach |
| topic | Classical Analysis and ODEs 42C40, 42B99, 65T60, 47N10, 65K10 |
| url | https://arxiv.org/abs/2311.12614 |