A New Nonlinear Sparse Optimization Framework in Ultrasound-Modulated Optical Tomography

In this work, a new nonlinear framework is presented for superior reconstructions in ultrasound-modulated optical tomography. The framework is based on minimizing a functional comprising of least squares data fitting term along with additional sparsity priors that promote high contrast, subject to the photon-propagation diffusion equation. The resulting optimization problem is solved using a sequential quadratic Hamiltonian scheme, based on the Pontryagin’s maximum principle, that does not involve semi-smooth calculus and is easy to implement. Furthermore, to improve resolution, the sequential quadratic Hamiltonian scheme is combined with an anisotropic diffusion filtering update scheme that preserves edges in the reconstructions whilst removing noise. Results of several experiments in 2D and 3D demonstrate the superiority of our new framework to obtain high quality reconstructions for complex objects with holes and inclusions.