Point spread function (PSF) estimation plays an important role in blind image deconvolution. It has been shown that incorporating Wiener filter, minimization of the predicted Stein’s unbiased risk estimate (p-SURE)—unbiased estimate of predicted mean squared error—could yield an accurate PSF estimate. In this paper, we provide a theoretical analysis for the PSF estimation error, which shows that the better deconvolution leads to more accurate PSF estimate. It motivates us to incorporate an $$\ell _1$$ ℓ 1 -penalized sparse deconvolution into the p-SURE minimization, instead of the Wiener-type filtering. In particular, based on FISTA—one of the most popular iterative $$\ell _1$$ ℓ 1 -solvers, we evaluate the p-SURE for each update, by Jacobian recursion and Monte Carlo simulation. Numerical results of both synthetic and real experiments demonstrate the improvements in PSF estimate, and therefore, deconvolution performance.