An evolutionary Bayesian search scheme for ultrasound modulated optical tomography

Ultrasound modulated optical tomography (UMOT) combines high optical contrast with high ultrasound resolution to image soft tissues. A focused ultrasound beam introduced to a specific region of interest (ROI) in the object modulates the mean position of the scattering centers locally. This in turn modulates the overall decay of the specific intensity of an incident coherent light beam as it passes through the insonified region. The inverse problem of UMOT aims to recover the mean-squared displacements of the scattering centers from the measured amplitude autocorrelation of light. We propose an evolutionary Bayesian search scheme to invert the measurements through repeated solves of the correlation diffusion equation so as to drive the resultant measurement-prediction misfit to a zero-mean Brownian process. The discretized parameter vector evolves as a stochastic process with respect to an iteration variable and follows a recursive prediction-update algorithm. The conventional multiplicative-weight-based Bayesian update schemes suffer from sample degeneracy and are consequently ill-equipped to solve large dimensional problems in imaging. The key idea of this work is to incorporate a derivative-free additive correction to the predicted parameter process via a gain term that is functionally analogous to the weights. The numerical results for simulated data indicate that the proposed scheme substantively improves the reconstruction accuracy vis-à-vis a popularly adopted regularized Gauss-Newton approach. The advantage of a derivative-free scheme is particularly highlighted in cases characterized by low sensitivity of measurements to variations in the parameters. Moreover, the proposed scheme circumvents the tedious Jacobian calculations involved in a Gauss-Newton approach.