Abstract
This paper proposes a multigrid inversion framework for quantitative photoacoustic tomography reconstruction. The forward model of optical fluence distribution and the inverse problem are solved at multiple resolutions. A fixed-point iteration scheme is formulated for each resolution and used as a cost function. The simulated and experimental results for quantitative photoacoustic tomography reconstruction show that the proposed multigrid inversion can dramatically reduce the required number of iterations for the optimization process without loss of reliability in the results.
Highlights
Quantitative photoacoustic (PA) imaging consists in producing the spatial distribution of the optical properties of tissue, including absorption coefficient μa and reduced scattering coefficient μs', from a measured absorbed energy distribution Hm (r) that can be obtained using conventional PA tomography [1,2,3]
Analytical solutions exist for simple cases [4,5,6], and numerical solutions are used for more realistic cases, using for example the finite difference method [7,8,9] or the finite element method [10,11,12]
Tomography reconstruction in which both the forward model of absorbed energy and the optimization scheme are expressed at multiple resolutions, hereafter called the “pure multigrid inversion algorithm.”
Summary
Quantitative photoacoustic (PA) imaging consists in producing the spatial distribution of the optical properties of tissue, including absorption coefficient μa and reduced scattering coefficient μs' , from a measured absorbed energy distribution Hm (r) that can be obtained using conventional PA tomography [1,2,3]. The main optimization schemes used in the bibliography embrace fixedpoint iteration and gradient-based optimization [13,14,15] All these inversion works were implemented on a fixed fine grid. We propose a framework of multigrid inversion for quantitative PA tomography reconstruction in which both the forward model of absorbed energy and the optimization scheme are expressed at multiple resolutions, hereafter called the “pure multigrid inversion algorithm.”. In the present pure multigrid inversion algorithm, both the forward and inverse problems are solved at different grid resolutions. It is assumed that the reduced scattering coefficient in the cost function has been known, as proposed in other studies [11,21,22]; only the absorption coefficient needs to be reconstructed and the nonuniqueness problem existing in a single measurement can be overcome [22,23]. The reconstruction process of this paper can be written as:
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