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Mathematical modeling in photoacoustic imaging of small absorbers. (English) Zbl 1257.74091

Summary: This paper is devoted to mathematical modeling in photoacoustic imaging of small absorbers. We propose a new method for reconstructing small absorbing regions inside a bounded domain from boundary measurements of the induced acoustic signal. We also show the focusing property of the back-propagated acoustic signal. Indeed, we provide two different methods for locating a targeted optical absorber from boundary measurements of the induced acoustic signal. The first method consists of a MUltiple SIgnal Classification (MUSIC)-type algorithm and the second one uses a multifrequency approach. We also show results of computational experiments to demonstrate efficiency of the algorithms.

MSC:

74J25 Inverse problems for waves in solid mechanics
74L15 Biomechanical solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
92C55 Biomedical imaging and signal processing
35C20 Asymptotic expansions of solutions to PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations