Fast diffraction-limited image recovery through turbulence via subsampled bispectrum analysis

Imaging through temporally changing aberrations is a common challenge that can be found in many different fields such as astronomy, long-range surveillance, and deep tissue bioimaging. Based on the notions originally developed in speckle interferometry, time-varying aberrations can be used to our advantage to obtain diffraction-limited resolution images through turbulence via bispectrum analysis. However, due to the heavy computational load brought on by the triple correlation and the phase extraction process, widespread use has been limited. Here, we demonstrate a Fourier domain subsampling scheme that can accelerate the speed of bispectrum analysis by more than 2 orders of magnitude. In contrast to other approaches for parallelization such as those based on Radon transform or image segmentation, our proposed method enables diffraction-limited imaging without suffering from resolution loss or image artifacts.