Special Section on Photoacoustic Imaging and Sensing

Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition

[+] Author Affiliations
Dimple Modgil, Patrick J. La Rivière

University of Chicago, Department of Radiology, 5841 South Maryland Avenue, Chicago, Illinois 60637

Bradley E. Treeby

Australian National University, College of Engineering and Computer Science, Canberra, Australian Capital Territory 0200, Australia

J. Biomed. Opt. 17(6), 061204 (May 07, 2012). doi:10.1117/1.JBO.17.6.061204
History: Received September 8, 2011; Revised November 10, 2011; Accepted November 28, 2011
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Abstract.  Attenuation effects can be significant in photoacoustic tomography since the generated pressure signals are broadband, and ignoring them may lead to image artifacts and blurring. La Rivière et al. [Opt. Lett.31(6), pp. 781–783, (2006)] had previously derived a method for modeling the attenuation effect and correcting for it in the image reconstruction. This was done by relating the ideal, unattenuated pressure signals to the attenuated pressure signals via an integral operator. We derive an integral operator relating the attenuated pressure signals to the absorbed optical energy for a planar measurement geometry. The matrix operator relating the two quantities is a function of the temporal frequency, attenuation coefficient and the two-dimensional spatial frequency. We perform singular-value decomposition (SVD) of this integral operator to study the problem further. We find that the smallest singular values correspond to wavelet-like eigenvectors in which most of the energy is concentrated at times corresponding to greater depths in tissue. This allows us to characterize the ill-posedness of recovering the absorbed optical energy distribution at different depths in an attenuating medium. This integral equation can be inverted using standard SVD methods, and the initial pressure distribution can be recovered. We conduct simulations and derive an algorithm for image reconstruction using SVD for a planar measurement geometry. We also study the noise and resolution properties of this image-reconstruction method.

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© 2012 Society of Photo-Optical Instrumentation Engineers

Citation

Dimple Modgil ; Bradley E. Treeby and Patrick J. La Rivière
"Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition", J. Biomed. Opt. 17(6), 061204 (May 07, 2012). ; http://dx.doi.org/10.1117/1.JBO.17.6.061204


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