We propose an unbiased estimator of the weighted mean squared error — Mallows’ statistics Cp — as a novel criterion for estimating a point spread function (PSF) from the degraded image only. The PSF is obtained by minimizing this new objective functional over a family of Wiener processings. Based on this estimated PSF, we then perform non-blind deconvolution using the popular BM3D algorithm. The Cp-based framework is exemplified with a number of parametric PSF’s, involving a scaling factor that controls the blur size. A typical example of such parametrization is the Gaussian kernel.
The experimental results demonstrate that the Cp-minimization yields highly accurate estimates of the PSF parameters, which also result in a negligible loss of visual quality, compared to that obtained with the exact PSF. The highly competitive results outline the great potential of developing more powerful blind deconvolution algorithms based on the Cp-estimator.