基于l_(2,p)-范数的ECT图像重建算法

针对电容层析成像系统图像重建过程中Tiknonov正则化解过度光滑引起的重建图像细节信息丢失问题,引入l_(2,p)(0p≤1)的混合范数作为正则化算法的数据项和正则化项。混合范数l_(2,p)利用了欧氏范数l_2的光滑性和分数范数l_p(0p≤1)的稀疏性,不仅比范数L_(2,1)具有更好的联合稀疏性,对噪声的抗干扰性也更强,进而针对l_(2,p)矩阵范数的非凸、非Lipschitz连续问题提出一种新的电容层析成像图像重建模型。实验结果表明,基于矩阵混合范数l_(2,p)极小化优化模型的正则化算法相比牛顿迭代、奇异值分解、共轭梯度算法具有更强的适应性,更高的图像分辨率及更好的成像质量。

l2,p-norm Based on the Image Reconstruction Algorithm for ECT

Aiming at the problem of the loss of the details of the reconstructed image caused by excessive smoothness of the Tiknonov regularization in the image reconstruction of electrical capacitance tomography (ECT) system,an image reconstruction model with norm l2,p (0 ＜p≤ 1) both on the data fidelity term and regularization term was introduced.The fractional matrix norm l2,p,which combines the smoothness of Euclid normand the sparsity of norm lp (0 ＜ p ≤ 1),has better joint sparsity and stronger reliability than matrix norm.A type of models based on l2.p matrix norm is presented,which is non-convex and non-Lipschitz continuous problem.The extensive experiments have showed,the l2,p-minimization,which has stronger adaptability,higher resolution and better image quality,is better than the Newton iterative method,conjugate gradient method and traditional singular value decomposition algorithm.