Generalized Ray Tracing with Basis functions for Tomographic Projections
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909782701506560 |
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| author | Haouchat, Youssef Kashani, Sepand Thévenaz, Philippe Unser, Michael |
| author_facet | Haouchat, Youssef Kashani, Sepand Thévenaz, Philippe Unser, Michael |
| contents | This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray tracing, which is one of the most efficient methods to compute line integrals. In our work, the cases in which the image is expressed as a spline are of particular relevance. The proposed implementation is applicable to any projection geometry as it computes the forward and backward operators over a collection of arbitrary lines. We validate our work with experiments in the context of inverse problems for image reconstruction and maximize the image quality for a given resolution of the reconstruction grid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Ray Tracing with Basis functions for Tomographic Projections Haouchat, Youssef Kashani, Sepand Thévenaz, Philippe Unser, Michael Image and Video Processing This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray tracing, which is one of the most efficient methods to compute line integrals. In our work, the cases in which the image is expressed as a spline are of particular relevance. The proposed implementation is applicable to any projection geometry as it computes the forward and backward operators over a collection of arbitrary lines. We validate our work with experiments in the context of inverse problems for image reconstruction and maximize the image quality for a given resolution of the reconstruction grid. |
| title | Generalized Ray Tracing with Basis functions for Tomographic Projections |
| topic | Image and Video Processing |
| url | https://arxiv.org/abs/2503.20907 |