不完全投影图像重建的压缩感知算法

Improved compressive sensing algorithm for CT image reconstruction with incomplete projection data

针对X射线激发的发光断层成像的经典扫描模式存在扫描时间过长的问题,基于传统的全变分最小化算法,提出一种改进的适应不完全投影条件下的压缩感知算法.改进算法结合非负约束条件下的代数重建法(ART)与梯度下降求解的全变分最小化过程,采用先进行多次ART迭代,再交替执行ART过程与全变分最小化过程的方式来求解约束最优化问题,讨论了改进算法在投影角度稀疏和投影角度受限两种不完全投影情况下的压缩感知重建,分析了调节因子和全变分最小化过程的迭代次数对重建图像质量的影响.基于Shepp-Logan头模型的仿真结果证明了改进算法的有效性.

Aiming at the problem of the long scanning time of the classical scanning modalities in X‐ray luminescence computed tomography and based on the traditional total variation minimization （ TVM ） algorithm , an improved compressive sensing （ CS ） algorithm for image reconstruction under incomplete projection situations is suggested and investigated . The algebraic reconstruction technique （ ART ） process under the non‐negative constraint and the total variation minimization process solved by the gradient descent method are combined in the improved algorithm . To solve the constrained optimization problem , the ART process is performed several times first and then alternates with the total variation minimization process . The CS reconstructions under two incomplete projection situations , few‐view projection and limited‐angle projection , are discussed , and the effects of the adjustment factor and the iterative number in the total variation minimization process on the performance are investigated . The effectiveness of the proposed method is demonstrated by the simulation experiments based on the Shepp‐Logan head phantom .