一种应用于高阶数据修复的非负稀疏Tucker分解算法

A sparse nonnegative Tucker decomposition for higher-order data inpainting

针对传统的张量填充算法对于不满足低秩条件的张量填充效果难以保证,本文采用张量分解的方法实现缺失张量的修复,即对传统Tucker分解算法进行改造,在其目标函数中增加对核心张量和系数矩阵的非负性以及核心张量的稀疏性约束,再利用凸优化理论中的交替近端梯度算法(APGM)对目标函数进行迭代寻优,在分解的同时实现缺失数据点的填充。医学图像、彩色图像和视频图像的修复结果表明,本文算法能够对高阶非负张量的缺失实现较好地修复,修复的视觉效果和技术指标都优于当前主流算法。

In this paper,a novel method for the factorization of a tensor with missing data is proposed for higher-order data inpainting. The proposed method enforces nonnegativity on core tensor and factor ma- trices, while sparseness on core tensor in Tucker factorization, and alternating proximal gradient method （APGM） can be used for minimizing the modified Tucker function. Numerical experiments are conducted in medical magnetic resonance imaging （MRI） images, color images and videos, and the simulation re- suits demonstrate that the proposed inpainting method outperforms the state-of-art tensor factorization and tensor completion based methods. It achieves higher performance in terms of peak signal to noise ra- tio （PSNR） ,structural similarity index t （SSIM） and root mean square error （RMSE）.