中文摘要：

针对单幅图像复原算法引入先验信息导致复杂度高、运算效率低的问题，提出了单幅模糊图像点扩散函数估计的梯度倒谱分析方法．首先给出了单幅模糊图像梯度倒谱估计其点扩散函数的基本原理，利用相位恢复策略复原了二维点扩散函数相位信息，实现了点扩散函数的快速估计；其次，为鉴别点扩散函数估计精度，建立了图像梯度保真约束的全变分正则化图像复原模型，并采用快速稳定收敛的交替方向策略优化能量函数；通过对仿真和实拍单幅模糊图像进行的测试实验结果表明，该方法快速准确地估计出点扩散函数，克服了传统复原算法收敛速度慢的缺点，有效抑制了振铃效应、保护了边缘信息，为大尺寸单幅图像复原的工程化实现提供了理论和技术基础．

英文摘要：

Since single image restoration algorithms using lots of priori information lead to high complexity and low computational effi- ciency, a gradient cepstrum analysis method is proposed to estimate the point spread function PSF for a single blurred image. Firstly, we present the basic principle of estimating PSF from gradient cepstrum of a single blurred image and use the phase retrieval algorithm to recover phase information of the two-dimensional PSF, which can obtain the estimated PSF rapidly, Secondly, to evaluate the accu- racy of the proposed PSF estimation method, the total variation regularized image restoration model coupling with an image gradient fidelity term is established and an alternating direction method with rapid and stable convergence is adopted to optimize the energy function. Both synthetic and real blurred images are tested to verify the performance of our scheme. Results show that our scheme not only can estimate the PSF rapidly and accurately so that it overcomes shortcomings of traditional algorithm with slow convergence, but also suppresses ringing effects to preserve information in edges. These advantages provide theoretical and technical foundation of the real engineering requirement in single image deblurring, especially for large scale images.