应用投影收缩的压缩感知锥束CT短扫描重建

Compressing-sensing cone-beam CT short-scan reconstruction based on projection-contraction

由于锥束CT成像系统在短扫描方式下无法获得完全投影数据,从而限制了图像重建的质量,本文提出了一种基于投影收缩的压缩感知锥束CT短扫描重建算法。考虑BB(Barzilai-Borwen)梯度投影算法的非单调收敛,分析了投影收缩法的预测校正特性,并将校正过程引入到压缩感知图像重建算法中。结合目标函数下降方向和凸集投影下降方向,校正BB梯度投影算法,改善BB梯度投影算法的非单调特性。应用该算法对模拟投影数据和仿体扫描数据分别进行了重建试验。模拟试验结果表明,在25个采样角度下,用提出算法重建图像的信噪比值比自适应最速下降-凸集投影算法、投影收缩算法和BB梯度投影算法的重建结果分别高出9.487 0、9.802 7、3.615 9dB。仿真试验结果表明:在少量投影角度下该算法重建结果有效抑制了条状伪影,清晰重建出边缘细节,极大提高了少量投影数据重建图像的质量。

To solve the problem of image reconstruction of incomplete projection data from a short-scan cone-beam CT, a novel cone-beam CT short-scan reconstruction algorithm was proposed based on pro- jection-contraction method. Aiming at the non-monotonic convergence of the Gradient-Projection Barz- ilari-Borwein （GPBB） algorithm, the predictor-corrector feature of projection-contraction method was analyzed and incorporated into compressed sensing image reconstruction algorithm. The objective func- tion descent direction and the projection onto convex sets descent direction were combined to correct the results of GPBB algorithm to improve the non-monotonic convergence of GPBB algorithm. Then, the experiments were conducted on simulated projection data and phantom scanning data. The simula- ted results for 25 sampling angles show that the signal-to-noise ratios of images reconstructed by PCBB algorithm are 9. 487 0, 9. 802 7, 3. 615 9 db higher than those of images reconstructed by Adap- tive Steepest Descent-Projection onto Convex Sets algorithm, projection contraction algorithm and GPBB algorithm, respectively. The simulation results indicate that when a small amount of projections are acquired, the new algorithm has effectively suppressed strip artifacts and the reconstructed images show clear edges. The algorithm can greatly improved the qualify of images reconstructed from few projection data.