Journal ArticleDOI
Determining a function from its mean values over a family of spheres
TLDR
An inversion algorithm is provided (with proof) when the mean values are known for all spheres centered on the boundary of D, with radii in the interval [0, diam(D)/2].Abstract:
Suppose D is a bounded, connected, open set in Rn and f is a smooth function on Rn with support in $\overD$. We study the recovery of f from the mean values of f over spheres centered on a part or the whole boundary of D. For strictly convex $\overline{D}$, we prove uniqueness when the centers are restricted to an open subset of the boundary. We provide an inversion algorithm (with proof) when the mean values are known for all spheres centered on the boundary of D, with radii in the interval [0, diam(D)/2]. We also give an inversion formula when D is a ball in Rn, $n \geq 3$ and odd, and the mean values are known for all spheres centered on the boundary.read more
Citations
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Journal ArticleDOI
Photoacoustic Tomography: In Vivo Imaging from Organelles to Organs
Lihong V. Wang,Song Hu +1 more
TL;DR: A review of the state of the art of photoacoustic tomography for both biological and clinical studies can be found in this paper, where the authors discuss the current state-of-the-art and discuss future prospects.
Journal ArticleDOI
Photoacoustic imaging in biomedicine
Minghua Xu,Lihong V. Wang +1 more
TL;DR: An overview of the rapidly expanding field of photoacoustic imaging for biomedical applications can be found in this article, where a number of imaging techniques, including depth profiling in layered media, scanning tomography with focused ultrasonic transducers, image forming with an acoustic lens, and computed tomography using unfocused transducers are introduced.
Journal ArticleDOI
Biomedical photoacoustic imaging
TL;DR: The underlying physical principles of the technique, its practical implementation, and a range of clinical and preclinical applications are reviewed.
Journal ArticleDOI
Multiscale photoacoustic microscopy and computed tomography.
TL;DR: PAT holds the promise of in vivo imaging at multiple length scales ranging from subcellular organelles to organs with the same contrast origin, an important application in multiscale systems biology research.
Journal ArticleDOI
Universal back-projection algorithm for photoacoustic computed tomography.
Minghua Xu,Lihong V. Wang +1 more
TL;DR: In this article, a universal back-projection algorithm for three-dimensional photoacoustic computed tomography is presented for three types of imaging geometries: planar, spherical, and cylindrical surfaces.
References
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Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
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TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
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Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
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The Mathematics of Computerized Tomography
TL;DR: In this paper, the Radon transform and related transforms have been studied for stability, sampling, resolution, and accuracy, and quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithm, for both standard problems and problems with incomplete data.
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Universal back-projection algorithm for photoacoustic computed tomography.
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