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Updated: Jul 31, 2025
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Three-dimensional Optical-resolution Photoacoustic Microscopy
Published on: May 3, 2011
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Analysis for Full-Field Photoacoustic Tomography with Variable Sound Speed
Linh Nguyen1, Markus Haltmeier2, Richard Kowar2
1Department of Mathematics, University of Idaho, 875 Perimeter Dr, Moscow, ID 83844, USA.
SIAM Journal on Imaging Sciences
|May 8, 2023
Summary
Photoacoustic tomography (PAT) offers non-invasive imaging by reconstructing wave equations. This study establishes mathematical foundations for full-field PAT, proving uniqueness and stability for variable sound speed, and introducing a time-reversal inversion method.
Area of Science:
- Biomedical imaging
- Wave physics
- Mathematical modeling
Background:
- Photoacoustic tomography (PAT) is a non-invasive imaging technique.
- PAT reconstructs wave equations from measurements outside an object.
- Standard PAT uses time-dependent signals, unlike the newer full-field detection.
Purpose of the Study:
- Establish mathematical foundations for full-field PAT.
- Investigate uniqueness and stability for variable sound speed.
- Introduce and analyze an exact inversion method for full-field PAT.
Main Methods:
- Developed mathematical framework for full-field PAT.
- Proved uniqueness and stability theorems for variable sound speed.
- Introduced and analyzed a time-reversal exact inversion method.
Main Results:
- Established mathematical foundations for full-field PAT with variable sound speed.
- Demonstrated uniqueness and stability of the full-field PAT problem.
- Showcased the convergence and effectiveness of the time-reversal inversion technique.
Conclusions:
- The full-field detection technique is suitable for PAT.
- The proposed time-reversal method enables high-resolution photoacoustic imaging.
- This work provides a solid mathematical basis for advanced PAT applications.
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