Parametric Blind Deconvolution of Microscopic Images: Further Results

Blind deconvolution microscopy, the simultaneous estimation of the specimen function and the point spread function (PSF) of the microscope is an under-determined problem with non-unique solutions. The non-uniqueness is commonly avoided by enforcing constraints on both the specimen function and the PSF, such as non-negativity and band limitation. These constraints are some times enforced in ad hoc ways. In addition, many of the existing methods for blind deconvolution estimate the PSF pixel by pixel thus greatly increasing the number of parameters to estimate and slowing the convergence of the algorithm. We derived a maximum-likelihood-based method for blind deconvolution in which we assume that the PSF follows a mathematical expression that depends on a small number of parameters (e.,g. less than 20). The algorithm then estimates the unknown parameters together with the specimen function. The mathematical model ensures that all the constraints of the PSF are satisfied and the maximum likelihood approach ensures that the specimen is non-negative. This parametric blind deconvolution method successfully removes out-of-focus blur but its degree of success depends on the features of the specimen. Specimen features that fall in mostly the null space of the PSF are more difficult to recover and make PSF estimation more difficult.