Abstract
The image reconstruction problem (or inverse problem) in photoacoustic tomography is to resolve the initial pressure distribution from detected ultrasound waves generated within an object due to an illumination by a short light pulse. Recently, a Bayesian approach to photoacoustic image reconstruction with uncertainty quantification was proposed and studied with two dimensional numerical simulations. In this paper, the approach is extended to three spatial dimensions and, in addition to numerical simulations, experimental data are considered. The solution of the inverse problem is obtained by computing point estimates, i.e., maximum a posteriori estimate and posterior covariance. These are computed iteratively in a matrix-free form using a biconjugate gradient stabilized method utilizing the adjoint of the acoustic forward operator. The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution in realistic measurement geometries and that the reliability of these estimates can be assessed.
Highlights
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines optical excitation with ultrasonic detection.1–7 This allows for both high contrast and high resolution to be achieved simultaneously
The image reconstruction problem in photoacoustic tomography is to resolve the initial pressure distribution from detected ultrasound waves generated within an object due to an illumination by a short light pulse
The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution in realistic measurement geometries and that the reliability of these estimates can be assessed
Summary
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines optical excitation with ultrasonic detection. This allows for both high contrast and high resolution to be achieved simultaneously. The eigenfunction expansion method is another approximate problem based method and it aims to solve the image reconstruction problem analytically as well In this method, the initial pressure is obtained as the series solution and series coefficients are calculated from measured pressure signals. A Bayesian approach to PAT was suggested.29 In this approach, all parameters are modeled as random variables and the formal solution of the inverse problem consists of a probability density for the initial pressure in each voxel of the reconstruction domain. All parameters are modeled as random variables and the formal solution of the inverse problem consists of a probability density for the initial pressure in each voxel of the reconstruction domain It combines the information obtained through the measurements, the forward model, and the prior model for unknown parameters.
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