Reciprocity relation for the vector radiative transport equation and its application to diffuse optical tomography with polarized light

Tricoli, Ugo; Macdonald, Callum M.; Silva, Anabela Da; Markel, Vadim A.

doi:10.1364/ol.42.000362

Cited by 15 publications

(18 citation statements)

References 18 publications

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“…The Green's function is calculated with N = 10 8 number of photons for a slab of thickness L = 1 * . In addition, the reciprocity relation [26] is applied to the Green's function propagating to the detector (although here we do not consider polarization). Then, an expansion in spherical harmonics of all angularly dependent functions is used; details of angular integration of (10) are explained in Appendix A.…”

Section: Resultsmentioning

confidence: 99%

“…We first make use of the reciprocity relation for the Green's function as introduced in Ref. [26] (although here we do not consider polarization). The sensitivity kernel can then be rewritten as As noted in Ref.…”

Section: Appendix: Angular Integrationmentioning

confidence: 99%

“…The Monte Carlo model as in Ref. [26] is used to calculate the Green's functions and the expansion in spherical harmonics with coefficients a LM up to l max = 15. The translational invariance is then used so that one coefficient is evaluated at the position r 2 which is just the position of the source translated by the vector joining the source and detector.…”

Section: Appendix: Angular Integrationmentioning

confidence: 99%

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Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

Tricoli¹,

Macdonald²,

Durdurán³

et al. 2018

Phys. Rev. E

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Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.

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Section: Resultsmentioning

confidence: 99%

Section: Appendix: Angular Integrationmentioning

confidence: 99%

Section: Appendix: Angular Integrationmentioning

confidence: 99%

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Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

Tricoli¹,

Macdonald²,

Durdurán³

et al. 2018

Phys. Rev. E

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“…[18][19][20][21][22][23][24] In some cases, where a linearized approximation is assumed for the inverse problem, the cost of rerunning the forward model can be avoided using techniques such as perturbation Monte Carlo (PMC) methods. 11,25,26 However, for the full nonlinear problem, although PMC can be used for calculation of the problem Jacobian, this has to be recomputed at each iteration of, for example, a Gauss-Newton optimization scheme. 27 In this study, if we are to accept a level of variance and imperfection in our forward/adjoint models, this of course raises the question of how much variance is acceptable in order for SGD to be successful?…”

Section: Stochastic-gradient Descentmentioning

confidence: 99%

“… 18 – 24 In some cases, where a linearized approximation is assumed for the inverse problem, the cost of rerunning the forward model can be avoided using techniques such as perturbation Monte Carlo (PMC) methods. 11 , 25 , 26 However, for the full nonlinear problem, although PMC can be used for calculation of the problem Jacobian, this has to be recomputed at each iteration of, for example, a Gauss–Newton optimization scheme. 27 …”

Section: Modeling and Inversion Problems In Optical Tomographymentioning

confidence: 99%

Efficient inversion strategies for estimating optical properties with Monte Carlo radiative transport models

2020

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Significance: Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop an approach to reduce this bottleneck, which has significant implications for quantitative tomographic imaging in a variety of medical and industrial applications. Aim: Our aim is to enable computationally efficient image reconstruction in (hybrid) diffuse optical modalities using stochastic forward models. Approach: Using Monte Carlo, we compute a fully stochastic gradient of an objective function for a given imaging problem. Leveraging techniques from the machine learning community, we then adaptively control the accuracy of this gradient throughout the iterative inversion scheme to substantially reduce computational resources at each step. Results: For example problems of quantitative photoacoustic tomography and ultrasoundmodulated optical tomography, we demonstrate that solutions are attainable using a total computational expense that is comparable to (or less than) that which is required for a single high-accuracy forward run of the same Monte Carlo model. Conclusions: This approach demonstrates significant computational savings when approaching the full nonlinear inverse problem of optical property estimation using stochastic methods.

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Image quality improvements of diffuse optical tomography by using multiple polarization components

Wen

Liu²,

Chen³

et al. 2022

Results in Optics

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Reciprocity relation for the vector radiative transport equation and its application to diffuse optical tomography with polarized light

Cited by 15 publications

References 18 publications

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion

Efficient inversion strategies for estimating optical properties with Monte Carlo radiative transport models

Image quality improvements of diffuse optical tomography by using multiple polarization components

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