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中文摘要：
在超分辨率影像重建中，基于最大后验估计（MAP）框架的重建方法具有较大的优势，应用非常广泛。然而，常用的迭代求解方法如最速下降法、共轭梯度法等收敛速度慢、处理时间长，经常难以满足实际处理的需要。该文在MAP框架的基础上，提出了基于不完全乔莱斯基分解预优共轭梯度的模氆求解方法，即在迭代求解过程中利用不完全乔莱斯基分解构造预优矩阵，降低系数矩阵的条件数，从而提高收敛速度，节省处理时间。实验结果证明，该方法是有效的、可行的。
英文摘要：
Super-resolution image reconstruction is a technique to estimate a high-resolution （HR） image from several low-resolution （LR） images, providing that the LR images are sub-sampled and displaced by different amounts of sub-pixel shifts. The maximum a posteriori （MAP） formulation has become one of the most popular approaches. However, the model-solved methods such as steepest decent （SD） and conjugate gradient （CG） have slowed convergent speed; much process time is still in need. To solve this problem, a preconditioned conjugate gradient method is given in this paper. This method uses incomplete Cholesky decomposition to get the preconditioner and to lower the condition number of the coefficient matrix. The proposed method is tested on aerial images and fruit images. The results indicate that it has quick convergent speed and process speed than SD method and CG method does.
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