Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur

Blind-deconvolution microscopy, the simultaneous estimation of the specimen function and the point-spread function (PSF) of the microscope, is an unde rdetermined problem with nonunique solutions that are usually avoided by en forcing constraints on the specimen function and the PSF. We derived a maxi mum-likelihood-based method for blind deconvolution in which we assume a ma thematical model for the PSF that depends on a small number of parameters ( e.g., less than 20). The algorithm then estimates the unknown parameters to gether with the specimen function. The mathematical model ensures that all the constraints of the PSF are satisfied, and the maximum-likelihood approa ch ensures that the specimen is nonnegative. The method successfully estima tes the PSF and removes out-of-focus blur. The PSF estimation is robust to aberrations in the PSF and to noise in the image. (C) 1999 Optical Society of America [S0740-3232(99)02110-9].