SURE-Type Functionals as Criteria for Parametric PSF Estimation

Point spread function (PSF) estimation plays an important role in blind image deconvolution. This paper proposes two novel criteria for parametric PSF estimation, based on Stein's unbiased risk estimate (SURE), namely, prediction-SURE and its variant. We theoretically prove the SURE-type functionals incorporating exact (complementary) smoother filtering as the valid criteria for PSF estimation. We also provide the theoretical error analysis for the regularizer approximations, by which we show that the proposed frequency-adaptive regularization term yields more accurate PSF estimate than others. In particular, the proposed SURE-variant enables us to avoid estimation of noise variance, which is a key advantage over the traditional SURE-like functional. Finally, we propose an efficient algorithm for the minimizations of the criteria. Not limited to the examples we show in this paper, the proposed SURE-based framework has a great potential for other imaging applications, provided the parametric PSF form is available.