Application of maximum-likelihood image-restoration in quantum-photon limited noncoherent optical imaging systems and their relation to nuclear-medicine imaging

Recent studies in maximum-likelihood (ML) image restoration have shown the feasibility of restoring positron-emission tomography images to a point beyond the classical limitation in resolution. These results have prompted a parallel study reported herein to determine if a similar method might provide superresolving image-restoration in quantum-photon limited noncoherent imaging systems. The challenge posed in this study is that of restoring Fourier components in the image that have been removed by the optical system. For clarity the authors summarize in this paper the derivation of the ML-based algorithm. Computer simulations are presented which show the feasibility of superresolution and the property of restoring missing Fourier components. Also shown are the results of a preliminary experiment of restoring the image from a defocused camera. Several potential applications that fit this model include fluorescence microscopy, astronomical imaging and infrared imaging