自适应步长非局部全变分约束迭代图像重建算法

针对计算机断层成像（CT）系统中，全变分（TV）迭代约束模型易于产生阶梯效应以及不能很好地保存图像中精细结构的问题，提出一种自适应步长的非局部全变分（NLTV）约束迭代重建算法。考虑到NLTV模型能较好保存和恢复图像细节以及纹理的特点，首先将CT模型当成在满足投影数据的保真项的解集中寻找满足特定正则项即NLTV最小化的解约束优化模型；然后，使用代数重建（ART）算法和分离布雷格曼（SB）来确保重建结果满足数据保真项和正则化项的约束；最后，以自适应最速下降-投影到凸集（ASD-POCS）算法作为基础迭代框架来重建图像。实验结果表明，在不含噪声的稀疏重建条件下，提出的算法使用30个角度的投影数据已经可以重建出理想的结果。在含噪稀疏数据重建实验中，该算法在30次迭代时已得到接近最终收敛的结果，且均方根误差（RMSE）是ASD-POCS算法的2.5倍。该重建算法能在稀疏投影数据下重建出精确的结果图像，同时改善了TV迭代模型的细节重建能力，且对噪声有一定的抑制作用。

Constraint iterative image reconstruction algorithm of adaptive step size non-local total variation

In order to solve the problem that the Total Variation (TV) iterative constraint model is easy to cause staircase artifact and cannot save the details in Computer Tomography (CT) images, an adaptive step size Non-Local Total Variation (NLTV) constraint iterative reconstruction algorithm was proposed. Considering the NLTV model is able to preserve and restore the details and textures of image, firstly, the CT model was regarded as a constraint optimization model for searching the solutions satisfying specific regular term, which means the NLTV minimization, in the solution set that satisfies the fidelity term of projection data. Then, the Algebraic Reconstruction Technique (ART) and the Split Bregman (SB) algorithm were used to ensure that the reconstructed results were constrained by the data fidelity term and regularization term. Finally, the Adaptive Steepest Descent-Projection Onto Convex Sets (ASD-POCS) algorithm was used as basic iterative framework to reconstruct images. The experimental results show that the proposed algorithm can achieve accurate results by using the projection data of 30 views under the noise-free sparse reconstruction condition. In the noise-added sparse data reconstruction experiment, the algorithm obtains the result similar to final convergence and has the Root Mean Squared Error (RMSE) as large as 2.5 times of that of ASD-POCS algorithm. The proposed algorithm can reconstruct the accurate result image under the sparse projection data and suppress the noise while improving the details reconstruction ability of TV iterative model.