Photoacoustic image reconstruction with uncertainty quantification
Photoacoustic tomography is a hybrid imaging technique that has various applications in biomedicine. In a photoacoustic image reconstruction problem (inverse problem), an initial pressure distribution is reconstructed from measured ultrasound waves which
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1 Department of Applied Physics, University of Eastern Finland, P.O.Box 1627, 70211 Kuopio, Finland Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom
Abstract— Photoacoustic tomography is a hybrid imaging technique that has various applications in biomedicine. In a photoacoustic image reconstruction problem (inverse problem), an initial pressure distribution is reconstructed from measured ultrasound waves which are generated by the photoacoustic effect induced by an optical excitation. In this work, the image reconstruction problem is approached in the framework of Bayesian inversion. The approach is tested with three dimensional numerical simulations. The initial pressure distribution is reconstructed in full-view and limited-view setups. In addition, the reliability of the obtained estimates is assessed. The numerical studies show that accurate estimates of the initial pressure distribution and uncertainty information can be obtained utilizing Bayesian approach.
backwards in time. In the model-based methods, the initial pressure distribution is obtained by minimizing the error between the measured signals and the signals computed by the photoacoustic forward model. Recently, PAT image reconstruction method utilizing a Bayesian approach was proposed [20]. The approach provides the estimates of the initial pressure distribution together with information about the reliability of these estimates. In this work, the approach is extended to three dimensions (3D). A matrix free method utilizing the adjoint of the forward operator is implemented. The approach is investigated using numerical simulations in different sensor geometries.
Keywords— photoacoustic tomography, inverse problems, Bayesian methods, uncertainty quantification
II. P HOTOACOUSTIC MODEL
I. I NTRODUCTION Photoacoustic tomography (PAT), also known as optoacoustic tomography, is a hybrid imaging modality that is characterized by high contrast and resolution [1, 2, 3]. PAT can provide structural, functional, and molecular information. Due to its many attractive features, its applications include e.g. detection of skin and breast cancer, imaging of vascular system and small animal imaging [1]. In PAT, a short pulse of visible or near-infrared light is used to irradiate the imaged object. Due to the photoacoustic effect, ultrasound waves are generated. The waves propagate to the surface of the object, where they are measured. From these time-varying measured pressure waves, an initial pressure distribution is reconstructed. This is also known as the acoustic inverse problem of PAT and it has been widely studied, see e.g. [4, 5, 6] and the references therein. The initial pressure distribution can be estimated using variety of reconstruction algorithms. Commonly used reconstruction algorithms are backprojection [7, 8, 9, 10], time reversal [11, 12, 13] and model based inversion approaches [14, 15, 16, 17, 18, 19]. The backprojection algorithms are based on analytical inversion formulae and are analogue
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