基于L_p算子的CT迭代重建算法研究

Research on CT Iterative Reconstruction Algorithms Based on L_p Operator

针对稀疏角度下的CT图像重建问题,E.Y.Sidky等人提出了ART-TV算法。该算法利用图像梯度具有稀疏性作为先验知识,每次迭代利用梯度下降法调整图像梯度的L1范数。论文在ARTTV算法的基础上,利用图像梯度的Lp(0<p<1)范数代替L1范数对图像进行重建,研究不同Lp(0<p<1)算子对图像重建效果的影响。实验表明,适当的p可以进一步提高图像重建质量。

For the problem of image reconstruction for sparse -view CT, E.Y.Sidky proposed the ART-TV algorithm.Using the prior information of images having sparse gradient -magnitude images , the al-gorithm performs each iteration of ART with a steepest -descent step to minimize the L1 norm of gradient -magnitude images.In this paper, the L1 norm is replaced by the Lp（1〈p〈1） norm to reconstruct images .The research focuses on the influence of different Lp（1〈p〈1） operators on images reconstruction quality .The sim-ulation and real data experimental results show that the proper p can improves the image reconstruction quality further.