Article

# A reconstruction algorithm for photoacoustic imaging based on the nonuniform FFT.

Department of Mathematics, University Innsbruck, 6020 Innsbruck, Austria.

IEEE transactions on medical imaging (Impact Factor: 3.54). 11/2009; 28(11):1727-35. DOI: 10.1109/TMI.2009.2022623 Source: PubMed

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**ABSTRACT:**Many modern imaging and remote sensing applications require reconstructing a function from spherical averages (mean values). Examples include photoacoustic tomography, ultrasound imaging or SONAR. Several formulas of the back-projection type for recovering a function in $n$ spatial dimensions from mean values over spheres centered on a sphere have been derived in [D. Finch, S. K. Patch, and Rakesh. Determining a function from its mean values over a family of spheres. SIAM J. Math. Anal., 35(5):1213-1240, 2004] for odd spatial dimension and in [D. Finch, M. Haltmeier, and Rakesh, SIAM J. Appl. Math. 68(2), pp. 392-412, 2007] for even spatial dimension. In this paper we generalize some of these formulas to the case where the centers of integration lie on the boundary of an arbitrary ellipsoid. For the special cases $n=2$ and $n=3$ our results have recently been established in [Y. Salman, arXiv:1208.5739 (math.AP), 2012].04/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish back-projection type inversion formulas that recover any initial data with support in $\Om$ modulo an explicitly computed smoothing integral operator $\K_\Om$. For circular and elliptical domains the operator $\K_\Om$ is shown to vanish identically and hence we establish exact inversion formulas of the back-projection type in these cases. Similar results are obtained for recovering a function from its mean values over circles with centers on $\partial \Om$. Both reconstruction problems are, amongst others, essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography.Computers & Mathematics with Applications 04/2013; 65(7). · 2.07 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper comprehensively reviews the emerging topic of optoacoustic imaging from the image reconstruction and quantification perspective. Optoacoustic imaging combines highly attractive features, including rich contrast and high versatility in sensing diverse biological targets, excellent spatial resolution not compromised by light scattering, and relatively low cost of implementation. Yet, living objects present a complex target for optoacoustic imaging due to the presence of a highly heterogeneous tissue background in the form of strong spatial variations of scattering and absorption. Extracting quantified information on the actual distribution of tissue chromophores and other biomarkers constitutes therefore a challenging problem. Image quantification is further compromised by some frequently-used approximated inversion formulae. In this review, the currently available optoacoustic image reconstruction and quantification approaches are assessed, including back-projection and model-based inversion algorithms, sparse signal representation, wavelet-based approaches, methods for reduction of acoustic artifacts as well as multi-spectral methods for visualization of tissue bio-markers. Applicability of the different methodologies is further analyzed in the context of real-life performance in small animal and clinical in-vivo imaging scenarios.Sensors 01/2013; 13(6):7345-84. · 1.95 Impact Factor

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