截断核范数低秩张量核矩阵图像修复算法  

Truncated Nuclear Norm Low-rank Tensor Kernel Matrix Image Repair Algorithm

作　　者：马瑞虾 张荣国[1] 胡静[1] 崔红艳 刘小君[2] MA Rui-xia;ZHANG Rong-guo;HU Jing;CUI Hong-yan;LIU Xiao-jun(School of Computer Science and Technology,Taiyuan University of Science and Technology,Taiyuan 030024,China;School of Mechanical Engineering,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]太原科技大学计算机科学与技术学院,山西太原030024 [2]合肥工业大学机械工程学院,安徽合肥230009

出　　处：《计算机技术与发展》2023年第6期54-60,共7页Computer Technology and Development

基　　金：国家自然科学基金(51875152);山西省自然科学基金(201801D121134)。

摘　　要：针对张量数据存在不完整和缺少项,导致图像修复过程中信息丢失的问题,提出了一种基于截断核范数和低秩张量核矩阵的图像修复算法TNN-LTKM(truncated nuclear norm low-rank tensor kernel matrix)。首先,引入张量截断核范数,对秩函数进行精确逼近,以增强优化模型的鲁棒性;其次,通过增加核心矩阵核范数扩展t-SVD中的张量核范数,定义了一个新的包含张量管秩和核矩阵秩的潜在核范数,来充分提取核张量中的低秩结构,消除冗余;接下来,采用增广拉格朗日法和交替方向乘子法对上述模型进行优化求解;最后,在ZJU、Berkeley和Kodak Lossless 3个数据集上进行实验验证,取相对平方误差、峰值信噪比、结构相似度和CPU运行时间4个评价指标,与现有的6种算法对比表明,TNN-LTKM算法在低采样率下有着良好的表现。An image restoration algorithm based on truncated nuclear norm low-rank tensor kernel matrix(TNN-LTKM)is proposed to solve the problem of information loss in image restoration due to incomplete and missing tensor.Firstly,a tensor truncated nuclear norm is introduced to accurately approximate the rank function to enhance the robustness of the optimization model.Secondly,by increasing the kernel norm of the core matrix to extend the tensor kernel norm in t-SVD,a new potential kernel norm containing the rank of the tensor tube and the rank of the kernel matrix is defined to fully extract the low-rank structure of the kernel tensor and eliminate redundancy.Then,the augmented Lagrange method and alternating direction multiplier method are used to optimize the above models.Finally,experiments were carried out on ZJU,Berkeley and Kodak Lossless data sets,and four evaluation indexes were taken,including relative square error,peak signal-to-noise ratio(PSNR),structure similarity and running time.Compared with the existing six algorithms,the TNN-LTKM algorithm has excellent performance at low sampling rates.

关 键 词：低秩图像修复 张量主成分分析 张量奇异值分解 矩阵核范数 张量截断核范数 

分 类 号：TP302.7[自动化与计算机技术—计算机系统结构]