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

Callum M Macdonald,Samuel Powell,Simon Arridge

doi:10.1117/1.jbo.25.8.085002

Abstract

.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 ultrasound-modulated 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.

Highlights

Inverse problems arise in many areas within biomedical optics, both for global characterization of optical properties of media and for image reconstruction, among other applications.[1]
If the forward problem is given by the solution to a partial differential equation (PDE), one appealing approach is to solve the forward and inverse problems simultaneously so that the forward problem is only approximately solved at intermediate stages in the algorithm; this approach is known as PDE-constrained optimization.[2,3,4]
The application of stochastic methods for the solution of PDEs is pertinent in problems involving diffuse optics, since the “gold standard” method of solving the radiative transfer equation (RTE)—which is the most generally applicable description of the underlying physics—is to use stochastic (Monte Carlo) techniques;[5] their use in such applications parallels their extensive employment in other fields such as neutron physics.[6]

Summary

Introduction

Inverse problems arise in many areas within biomedical optics, both for global characterization of optical properties of media and for image reconstruction, among other applications.[1] Inverse problems are often considered as optimization problems, solved by deriving the gradient of an objective function and iteratively descending through the solution space. This process requires repeated solutions of forward and corresponding adjoint problems that are often computationally demanding in their own right. The practicality of Monte Carlo techniques has been significantly boosted by recent advances in computational hardware developments, in the application of parallelization.[9,10] Other approaches to improve their computational performance have been explored, such as the introduction of perturbation techniques[11] or variance reduction techniques.[12,13] even when the aforementioned approximations to the RTE are reasonable, Monte Carlo solutions may offer an attractive alternative to the use of deterministic techniques such as the finite element method, when the complexity of the geometry or probe requires a high-density discretization of the spatial domain

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Results

Discussion

Conclusion