Mallows’ statistics CL: A novel criterion for parametric PSF estimation

• Mallows’ statistics CLCL as a novel criterion for PSF estimation.
• An adaptive regularizer is applied to improve estimation accuracy.
• This proposed framework is applicable for any specific parametric form of PSF.

Considering blind image deconvolution as a statistical estimation problem, we propose an unbiased estimator of the prediction error – Mallows’ statistics CLCL – 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 smoother filterings (with frequency-dependent regularization term). We then perform non-blind deconvolution using the popular BM3D algorithm. The CLCL-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 show that the CLCL-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 demonstrate the great potential of developing more powerful blind deconvolution algorithms based on the CLCL-estimator.