迭代张量高阶奇异值分解的图像恢复方法

为了有效地对图像缺失数据进行恢复, 提出一种迭代张量高阶奇异值分解（HOSVD）图像缺失数据恢复方法。该方法首先利用拉格朗日乘子方法将张量核范数目标函数进行子问题分解操作, 简化了求解过程, 然后迭代地采用张量高阶奇异值分解阈值方法进行子问题求解, 最终得到恢复后的图像缺失数据。将矩阵奇异值阈值算法进行扩展而得的HOSVD阈值方法充分利用了图像内部和图像与图像之间的多重约束关系, 大大提高了恢复精度。模拟实验和真实图像实验结果显示该方法具有良好的缺失数据的恢复性能。

Iterative tensor high-order singular value decomposition method for image restoration

To effectively restore the missing value in images, this paper proposed the iterative tensor high-order singular value decomposition(HOSVD) method. To simplify the solving process, the method divided the tensor nuclear norm objective function into sub-problems based on the Lagrange multiplier method. And it solved the sub-problems by using tensor HOSVD thresholding approach iteratively. Finally, it recovered the missing value. The proposed method can make full use of the multiple constrain relations among inter-frame and intra-frame images which can greatly improve the recovery precision. Simulation and real image experiment results demonstrate that this method has good restoration properties of missing value.