中文摘要：

传统的加权最小二乘法、惩罚项加权最小二乘法虽然能够重建得到较好质量的图像，但在欠采样的条件下不能很好的拟制噪声．全变差作为正则项已广泛用于图像重建中，利用图像稀疏的先验知识能够在欠采样的条件下很好的重建图像．本文结合加权最小二乘法和全变差的优点，构造了基于全变差正则项的加权最小二乘法目标函数，运用交替求解的方法，将目标函数分解为求解二次优化和全变差正则化的优化问题，并分别用超松弛迭代方法和梯度下降法求解这两个优化问题．采用Zubal模型对该算法与传统算法进行仿真验证比较，并用相关系数、方差、信噪比等参数描述图像重建质量．结果表明在欠采样条件下，该算法能够更好的拟制噪声，重构效果比传统的有明显地提高．

英文摘要：

The traditional techniques of PET image reconstruction such as the least-squares and the penalty weighted least- squares can obtain high quality image,but they can＇ t suppress the noise well under the limited angle situation. The total variation （TV） was used widely as penalty in image reconstruction, which applied the sparsity prior of image and could accurately reconstruct the image from the limited angle （ a small quality of measurement）. This article combined the advantages of the weighted least squares and total variation and constructed the objective function based on them, and solved the objective function using the alternate methods. The objective function was decomposed into two simple optimization problems for solving quadratic optimization and total variation regularization, the over relaxation method and the gradient descent method were used to solve these two optimization prob- lems. Simulations using Zubal model were utilized to estimate the qualities of the reconstructed images, the evaluation parameter~ in- chided CORR, VAR and SNR. The experimental results show the proposed algorithm has better performance in noise suppression and good reconstruction effect under limited angle situations.