[OPTICAL REVIEW Vol. 20, No. 5 (2013) 442-451]

© 2013 The Japan Society of Applied Physics

## Numerical Evaluation of Linearized Image Reconstruction Based on Finite Element Method for Biomedical Photoacoustic Imaging

Shinpei OKAWA^{*}, Takeshi HIRASAWA, Toshihiro KUSHIBIKI, and Miya ISHIHARA

Department of Medical Engineering, National Defense Medical College, Tokorozawa, Saitama 359-8513, Japan

(Received February 19, 2013; Revised May 10, 2013; Accepted July 2, 2013)

An image reconstruction algorithm for biomedical photoacoustic imaging is discussed. The algorithm solves the inverse problem of the photoacoustic phenomenon in biological media and images the distribution of large optical absorption coefficients, which can indicate diseased tissues such as cancers with angiogenesis and the tissues labeled by exogenous photon absorbers. The linearized forward problem, which relates the absorption coefficients to the detected photoacoustic signals, is formulated by using photon diffusion and photoacoustic wave equations. Both partial differential equations are solved by a finite element method. The inverse problem is solved by truncated singular value decomposition, which reduces the effects of the measurement noise and the errors between forward modeling and actual measurement systems. The spatial resolution and the robustness to various factors affecting the image reconstruction are evaluated by numerical experiments with 2D geometry.

Key words: photoacoustic imaging, photon diffusion equation, wave equation, finite element method, truncated singular value decomposition, inverse problem

^{*}E-mail address: okawa@ndmc.ac.jp