The Diffusive Ultrasound Modulated Bioluminescence Tomography with Partial Data and Uncertain Optical Parameters
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911827584090112 |
|---|---|
| author | Yang, Tianyu Yang, Yang |
| author_facet | Yang, Tianyu Yang, Yang |
| contents | The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse problem with internal data, and derive a reconstruction procedure to recover the bioluminescent source. Subsequently, an uncertainty quantification estimate is established to assess the robustness of the reconstruction. To facilitate practical implementation, we discretize the diffusive model using the staggered grid scheme, resulting in a discrete formulation of the UMBLT inverse problem. A discrete reconstruction procedure is then presented along with a discrete uncertainty quantification estimate. Finally, the reconstruction procedure is quantitatively validated through numerical examples to demonstrate the efficacy and reliability of the proposed approach and estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Diffusive Ultrasound Modulated Bioluminescence Tomography with Partial Data and Uncertain Optical Parameters Yang, Tianyu Yang, Yang Analysis of PDEs Numerical Analysis 35R30 The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse problem with internal data, and derive a reconstruction procedure to recover the bioluminescent source. Subsequently, an uncertainty quantification estimate is established to assess the robustness of the reconstruction. To facilitate practical implementation, we discretize the diffusive model using the staggered grid scheme, resulting in a discrete formulation of the UMBLT inverse problem. A discrete reconstruction procedure is then presented along with a discrete uncertainty quantification estimate. Finally, the reconstruction procedure is quantitatively validated through numerical examples to demonstrate the efficacy and reliability of the proposed approach and estimates. |
| title | The Diffusive Ultrasound Modulated Bioluminescence Tomography with Partial Data and Uncertain Optical Parameters |
| topic | Analysis of PDEs Numerical Analysis 35R30 |
| url | https://arxiv.org/abs/2404.03124 |