白敏茹,黄孝龙,顾广泽,赵雪莹.基于张量秩校正的图像恢复方法[J].湖南大学学报:自然科学版,2016,43(10):155~160
基于张量秩校正的图像恢复方法
Tensor Rank Corrected Procedure for Image Restoration
  
DOI:
中文关键词:  图像恢复  张量奇异值分解  张量秩校正  张量近似点算法
英文关键词:image restoration  t-SVD  tensor rank-correction model  tensor proximal point algorithm
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作者单位
白敏茹,黄孝龙,顾广泽,赵雪莹 (湖南大学 数学与计量经济学院,湖南 长沙410082) 
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中文摘要:
      针对医学图像和视频图像的恢复问题,基于张量表示,研究有限样本下的低秩张量数据恢复问题,在张量奇异值分解(t-SVD)理论的基础上,提出了张量秩校正模型和两阶段张量秩校正方法,第一阶段是用张量核范数最小化模型求得预估解,第二阶段,根据预估解,求解张量秩校正模型,获得更高精度的解.构建了求解张量秩校正模型和张量核范数最小化模型的张量近似点算法,使得可以在实数域上对张量直接进行计算,并且从理论上证明了该算法的收敛性.通过对医学图像和视频图像的数值仿真实验,验证了本文所提出模型和方法的有效性,实验结果显示,张量秩校正模型和方法能够取得更高的恢复精度.
英文摘要:
      Tensor-based restoration of medical images and video images was studied with limited samples. On the basis of the theory of tensor singular value decomposition (t-SVD), a tensor rank-correction model (CRTNN) was proposed to correct the tensor nuclear norm minimization model (TNN). A two-stage rank correction method is given as follows: the first stage is used to generate a pre-estimator by solving the TNN model, and the second stage is to solve the CRTNN model to generate a high-accuracy recovery by the pre-estimator. A tensor proximal point algorithm was proposed to solve the CRTNN model and the TNN model, making it possible to calculate tensor directly in the real field. The convergence of the algorithm was proved in theory. Numerical experiments of medical images and video images verify the efficiency of the proposed model and method. The experiment results show that tensor rank-correction model and method can achieve higher-accuracy recovery.
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