基于张量理论在高维图像处理中的应用, 提出一种张量模式的稀疏表示方法, 以便有效地去除肺部CT序列图像的噪声, 增强图像的有用信息。首先, 设计了张量模式的正交匹配追踪法(TOMP)来表达稀疏系数; 构建了高维K-奇异值分解法(HOK-SVD)用于字典更新。然后, 对张量乘法的参数进行优化, 即通过构造三维灰度共生矩阵, 建立三维纹理特征与张量乘法模式之间的数学模型。最后, 将这种方法应用于LIDC数据库的150组CT序列图像的预处理, 对各算法的稀疏表示效果进行评价。与当前应用的其他方法相比, 本文提出的高维K-SVD算法的的峰值信噪比提高了1.5%, 平均误差降低了1.2%; 在此预处理基础上进行的图像分割结果表明: 图像的边缘偏移误差下降了3.0%, 体积重叠率提高了1.2%。上述结果显示基于张量的方法可以更精确地完成对三维CT图像序列的稀疏表示。

On the basis of tensor-based theory applied to the high-dimensional image processing, a tensor-based sparse representation algorithm was proposed to preprocess lung CT images and to enhance the useful information for the images. Firstly, a Tensor-based Orthogonal Matching Pursuit (TOMP) was designed for sparse representation and a Higher-order K-Singular Value Decomposition (K-HOSVD) was constructed for updating the dictionary. Then, the main parameters of the tensor multiplication was optimized. It means that the 3D gray-level co-occurrence matrix was constructed and the relationship between tensor multiplication model and texture features was established. Finally, the proposed method was used in 150 sets of lung CT images from LIDC database and the sparse representation performance of the proposed scheme was evaluated. The results from proposed algorithm show that the Peak Signal to Noise Ratio (PSNR) is increased by 1.5% and the Mean Square Error (MSE) is decreased by 1.2% as compared with that of other common schemes. Furthermore, the edge bias error is decreased by 3.0% and the volume overlap is increased by 1.2% as compared with that of preprocessing segmentation result. The conclusion indicates that the proposed algorithm is more suitable for the sparse representation of three-dimensional images.