Strict a priori constraints for maximum-likelihood blind deconvolution

We present a maximum-likelihood approach to improve blind deconvolution of an image. Blind deconvolution is performed through the minimization of an error function by use of the conjugate gradient method, as suggested by Lane [ J. Opt. Soc. Am. A9, 1508 ( 1992)]. We show how to implement strict constraints, such as image positivity, using a reparameterization. As an example, the point-spread function can be described by phase aberrations in the case of speckle imaging. The improvement brought by the use of strict rather than loose constraints is demonstrated on both simulated and real data. Different noise levels and object types are considered.