本文建立一种融合基于 DCT 变换的相似块张量 T-SVD 分解稀疏正则项的 图像去噪模型. 模型利用相似块张量基于 DCT 变换的 T-SVD 分解给出稀疏分解 方式. 该分解定理类似于矩阵的奇异值分解可自适应地给出张量的稀疏表示方式, 模型利用相似块张量分解后所具备的稀疏性质建立正则项, 使用增广拉格朗日方 法进行求解, 最后给出模型的数值试验结果. 对比经典的 BM3D 去噪方法, 本文 模型中张量变换的基底随数据更新, 这保证稀疏正则项充分发挥作用, 进而提升 去噪速度. 试验结果表明模型对于分片常值图像的去噪效果非常显著, 优于目前 的很多著名去噪方法, 我们从理论上给出上述实验现象的分析. 另外, 我们还发现 对于纹理图像去噪效果显著的基于块匹配的 SVD 算子构建正则项的图像去噪模 型本质上对应着张量的 HOSVD 分解. 最后, 我们还将模型与基于学习的去噪网 络做对比, 试验结果表明对于分片常值图像该模型具有更好的数值表现.

In this paper, an image denoising model combined with sparse term which is built by DCT based T-SVD decomposition of similar block tensor is established. The model uses DCT based T-SVD decomposition to give sparse decomposition of similar block tensor. The decomposition theorem is similar to the singular value de- composition theorem of matrix, which can adaptively give the sparse representation of tensor. The model uses the sparse property of similar block tensor decomposi- tion to establish the regular term, uses the augmented Lagrangian method to solve the problem, and finally gives the numerical test results of the model. Compared with the classical BM3D denoising methods, the base of tensor transformation in this model is updated with the data to ensure that the sparse regular terms play a full role and improve the denoising speed. The experimental results show that the denoising effect of the model for the segmented constant value images is very out- standing, which is better than many famous denoising methods. We theoretically give the analysis of the above experimental phenomena. In addition, we also find that the block matching local SVD operator based sparsity and TV regularization denoising model with excellent denoising effect for texture images essentially corre- sponds to tensor HOSVD decomposition. Finally, we also compare the model with the learning based denoising network, our model has better numerical performance for segmented constant value images.