基于小波框架的有限角度CT重建算法

针对有限角度CT重建问题，结合压缩传感相关理论，提出了基于小波框架的有限角度CT迭代重建算法．该算法利用小波框架的冗余性及框架系数稀疏性原理，首先建立了小波框架图像重建模型，通过共轭梯度法求解投影方程，得到重建图像，然后通过分裂Bregman迭代法对重建图像的小波框架系数进行阈值收缩，减小图像L1范数，提高重建精度．实验结果表明在有限的投影数据下该算法重建出的图像内部结构边缘清晰，对比度高，重建误差低，对噪声有一定的抑制作用．

Limited angle computed tomography reconstruction algorithm based on wavelet frame

Focusing on the limited angle computed tomography （CT） reconstruction and combining the compressed sensing correlated theory, an iterative method was proposed based on the wavelet frame regularization. By taking advantage of the wavelet frame redundancy and framework coefficient sparsity theory, the wavelet frame image reconstruction model was first established to solve the project equation using the conjugate gradient method, thus the reconstructed image was got. And next, the threshold of wavelet frame coefficients of the reconstructed image was shrunk in the split Bregman iteration, so as to penalize the L1 norm of the image and improve accuracy of reconstruction. Experimental results show that the proposed algorithm can achieve better quality with limited projection data： the internal edge of the reconstructed image is clear, with a high contrast ratio and low error of reconstruction, having restraining effect on noise to a certain degree.