Regularizing strategy for image restoration and wave-front sensing by phase diversity

Abstract

Restoring images blurred by an unknown optical system is a problem of interest in image processing and, in particular, in terrestrial astronomy, in which the incoming radiation from celestial objects is contaminated in an unforeseeable way by passing through the atmosphere in turbulent motion. Here a blind deconvolution method of image restoration of the phase-diversity class is presented. Numerical analysis clearly shows that the algorithm is capable of finding both the unknown incoherent object and the point-spread function, which is considered a function of a phase-aberration term only, from multiple images and in the absence of a reference source. Noise and measurement errors, such as calibration errors of the detecting optical system, are explicitly taken into account. Exploiting both the physical constraint on the optical path disturbance and a regularizing functional yields a rigorously stable problem.