Abstract

Previous work on maximum-likelihood image restoration for noncoherent imagery is extended to problems of blind deconvolution, in which the impulse response of the system is assumed to be unknown. The applications that motivate this study are both conventional and confocal fluorescence microscopy. The methodology incorporates the iterative expectation-maximization algorithm. Although the precise impulse response is assumed to be unknown, some a priori information about the impulse response is needed. In this study, the circular symmetry of the impulse response is employed to provide the needed information. The iteration of the algorithm is described in foursteps. In the first and second steps, the complete data of the true image and the impulse response are estimated by means of expectation operations based on the estimates of the true image and impulse response from the previous iteration. The complete data set is a postulated data set, from which derivation of a maximum-likelihood estimate of the true image and impulse response is straightforward. In the third and fourth steps, the maximum-likelihood estimates of the true image and impulse response are found from the postulated complete data that were estimated in the first two steps. Preliminary simulations demonstrate the potential usefulness and limitations of these methods.

© 1990 Optical Society of America