Fast Optimization Schemes for Phase Recovery in Bispectral Imaging

Speckle interferometry is a common method used to obtain astronomical images using ground-based telescopes to image through a turbulent atmosphere-telescope system. However, when imaging more complicated astronomical objects such as satellites, speckle interferometry methods necessitate the separate recovery of the object’s Fourier phase to obtain more detailed images. Bispectral methods are one approach to solving this complementary problem of phase recovery in speckle interferometry. They retrieve an object’s Fourier phase by matching it to the object’s bispectrum, a collectable statistical quantity from the speckle data. Mathematically, phase retrieval from the bispectrum can be formulated as a large-scale, non-linear least-squares problem. We consider several optimization schemes from the literature for solving this phase retrieval problem. In particular, we focus on accelerating the speed and convergence of this optimization while maximizing the quality of the recovered image through efficient implementation, Hessian based optimization, and appropriate regularization.