Simultaneous reconstruction of absorption, scattering and anisotropy factor distributions in quantitative photoacoustic tomography

Abstract

We present for the first time the simultaneous reconstruction of three optical parameters distributions of biological tissues namely, the absorption µ a and scattering µ s coefficients, as well as the anisotropy factor g of the Henyey-Greenstein phase function as a new optical contrast. The 2D images are obtained from the simulation experiments and multi-source quantitative photoacoustic tomography with the radiative transfer equation (RTE) as light transport model. The image reconstruction method is based on a gradient-based optimization scheme. The adjoint method applied to the RTE is used to efficiently compute the gradient of the objective function. The results show simultaneous reconstructions of the three optical properties even with noisy data. The crosstalk problem between the three parameters is highlighted. Superior quality images are obtained for µ a compared to those of µ s and g. Moreover, our algorithm allows reconstructing inserts-like heterogeneities with very good spatial resolution and qualitative accuracy.

New gas radiation model based on the principle of weighted sum of gray gases. Application to CO 2 –H 2 O mixtures at high temperature

“…The objective function J (39) will be minimized by means of the inverse algorithm when Eq. ( 42) is satisfied [34,35].…”

“…A gradient-based optimization algorithm using the quasi-Newton method with Lm-BFGS [34,35,38] was used to iteratively minimize the objective function J given by Eq. ( 16).…”

“…The simultaneous estimation of the twelve parameters in the proposed gas radiation forward model needs a scaling procedure [35] since the type and the order of magnitude of the parameters to be estimated are different. Accordingly, the components of the objective function gradient for each parameters are also different by about the same order of magnitude, which is detrimental to the solution of the inverse problem with a gradient-based optimization algorithm.…”

“…The inverse problem is introduced to estimate the parameters of the forward new gas radiation model. A Lagrangian formulation is adopted to accurately establish the adjoint state of the non-gray RTE and the objective function gradients [34,35].…”

Quantitative photoacoustic tomography: modeling and inverse problems

“… 141 , it was shown that the nonuniqueness can be overcome using multiple optical illuminations to obtain more data. One way to achieve this would be by illuminating the target from different directions 141 , 143 , 150 , 162 – 168 or using light patterns. 169 This approach has not yet been exploited experimentally, perhaps because experimentalists are concerned to obtain the maximum signal possible given the weakness of the photoacoustic effect, and so try to flood the tissue with light from as many directions as possible.…”