  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 a novel approach to reduce this
bottleneck which has significant implications for quantitative tomographic
imaging in a variety of medical and industrial applications. 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, in order to substantially reduce computational resources at
each step. 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. This approach demonstrates significant computational savings
when approaching the full non-linear inverse problem of optical property
estimation using stochastic methods.
