PSF (point spread function) estimation plays an important role in blind image deconvolution. It has been shown in our previous work that minimization of the Stein’s unbiased risk estimate (SURE) – unbiased estimate of mean squared error (MSE) – could yield an accurate PSF estimate. In this paper, we show that the PSF estimation error is upper bounded by the deconvolution accuracy and the mismatch between the assumed PSF parametric form and the underlying true one. For this reason, we incorporate the ℓ1{\ell_{1}}-penalized sparse deconvolution into the SURE instead of previously used Wiener filter. In particular, we apply the iterative soft-thresholding algorithms to solve ℓ1{\ell_{1}}-minimization, and develop recursive evaluations of SURE, which is then shown to converge to the existing theoretical result. In practical implementations with large-scale data, we apply the Monte-Carlo simulation to avoid the explicit matrix operation. Numerical examples demonstrate the improvements of PSF estimate, and the resulting deconvolution performance.

中文翻译：

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基于递归SURE的参数PSF估计的稀疏反卷积

PSF（点扩展函数）估计在盲图像反卷积中起重要作用。在我们先前的工作中已经表明，斯坦因的无偏风险估计（SURE）（均方误差的无偏估计）的最小化可以产生准确的PSF估计。在本文中，我们证明了PSF估计误差的上限是解卷积精度以及假定的PSF参数形式与基础真实形式之间的不匹配。因此，我们将ℓ1{\ ell_ {1}}惩罚的稀疏反卷积合并到SURE中，而不是以前使用的Wiener滤波器。特别是，我们应用迭代的软阈值算法来解决ℓ1{\ ell_ {1}}-最小化问题，并开发了SURE的递归评估，然后证明了该评估可以收敛到现有的理论结果。在具有大规模数据的实际实现中，我们应用蒙特卡洛模拟来避免显式矩阵运算。数值示例说明了PSF估计的改进以及由此产生的反卷积性能。