Restoration of differently blurred versions of an image with measurement errors in the PSF's

Restoration of an object from T observations is considered. Each image is distorted by a different deterministic blur and additive noise. The point spread function (PSF) for each observation is unknown, however, a noisy measurement of it is available. Taking the errors in measurements of the PSF's into consideration, the maximum likelihood and the Wiener filters are derived. It is shown that these filters give better results than the regression filter and the conventional Wiener filter, i.e., the one which ignores the presence of the noise in the PSF's. The consistency and the ill-conditioning characteristics of the filters are discussed. Regularized forms for these filters are also obtained.