基于L1与TV正则化的改进图像重建算法

Improved Image Reconstruction Algorithm Based on L1-Norm and TV Regularization

针对不完全投影数据图像重建中出现伪影和噪点的问题,提出了L1与TV同时进行正则化的图像重建模型。基于该重建模型,通过将Bregman迭代和TV软阈值滤波相结合,进一步提出了一种图像重建算法。该算法首先将投影数据通过优化的Bregman迭代算法进行初步重建,然后使用TV软阈值滤波对改造的全变分模型进行二次重建,最后判断是否满足设定的收敛阈值,若满足则结束重建,输出重建图像,否则重复进行上述两步操作,直至迭代完成。实验采用不添加噪声的Shepp-Logan模型与添加噪声的Abdomen模型来验证算法的有效性,证明了所提出的算法在视觉上均优于ART,LSQR,LSQT-STF,BTV等典型的图像重建算法,同时通过多项评价指标对比表明所提出的算法有明显优势。实验结果表明,所提算法在图像重建中能够有效去除条形伪影并保护图像细节,同时具有良好的抗噪性。

Concerning the streak artifacts and noise in the image reconstruction for incomplete projection data,this paper presented a image reconstruction model integrating L1 and TV regularization.Based on this model,this paper proposed a new image reconstruction method combining Bregman iteration and TV soft-thresholding filter.In the proposed method,the projection data are first applied to carry out preliminary reconstruction through Bregman iteration,and then the iterative results are used to minimize the TV model.At last,by repeating the above two steps,the reconstructed ima-ge can be obtained.To demonstrate its effectiveness,the Shepp-Logan model without noise and the Abdomen model with noise were employed to take experiments.The proposed algorithm not only has better visual effects,but also has more excellent performance compared with the existing algorithms such as ART,LSQR,L1 and BTV etc.Experimental results show that the proposed algorithm can well preserve image details and edges,and possesses good anti-noise capability,while eliminating streak artifacts effectively.