张量环因子非凸秩约束的高光谱图像超解析

Hyperspectral Image Super Resolution via Nonconvex Low-rank Constraint of Tensor Ring Factors

针对高光谱图像超解析问题,提出了一种联合子空间表示、非局部相似性和张量环因子非凸秩约束的超谱-多谱融合模型。首先,基于高光谱图像的全局谱低秩特性,利用原始低空间分辨率高光谱谱域信息将其降维至子空间表示;随后,针对视觉对像在非局部维度上的强相关性,利用多光谱图像的空间冗余信息将降维后子空间图分成多个相似patch组,并对其施加张量环分解挖掘低秩信息。其中,对分解因子添加基于t-SVD的张量核范数约束,并利用非凸log函数逼近本质秩函数,代替传统凸张量核范数约束,在保持其光谱-空间结构的基础上,避免凸函数过度惩罚较大奇异值所导致的有偏解问题。最后,建立完整的融合模型,并采用交替方向乘子法进行变量优化求解。通过多组实验进行验证,结果表明所提模型提高了视觉质量,与现有最新的融合模型相比,该方法在定量评价的数值结果上也有明显优势。新模型充分考虑了高光谱图像的全局谱低秩性,并结合了非局部相似先验与张量环分解的非凸张量因子秩,能够有效实现高光谱图像的超分辨率重构。

Hyperspectral Image(HSI)is composed of multiple discrete bands with specific frequencies.It not only contains rich spectral information but also provides real scenes that cannot be captured by human eyes,which is conducive to accurately target recognition.It has been widely used in earth remote sensing tasks such as compressed sensing,target classification,etc.However,limited by solar irradiance,optical imaging mechanism,and other factors,the equipment usually sacrifices part of the spatial resolution to ensure a high spectral resolution,which greatly limits the subsequent processing and application accuracy of spectral images.In contrast to HSI,Multispectral Image(MSI)obtained by multispectral sensor has high spatial resolution but low spectral resolution.To date,the fusion of High Spatial Resolution Multispectral Image(HR-MSI)and Low Spatial Resolution Hyperspectral Image(LR-HSI)in the same scene into High Spatial Resolution Hyperspectral Image(HR-HSI)is a common method to realize high-quality HSI reconstruction.In the early methods,multidimensional HSI data are often transformed into matrix processing.However,HSI is essentially a kind of 3D data with two spatial dimensions and one spectral dimension.Transforming multidimensional HSI data into matrix will inevitably destroy its spectral-spatial structural correlation and reduce the model performance.Tensor representation can effectively preserve the inherent structural information of spectral images.The method based on tensor decomposition has also become one of the effective schemes to solve the problem of HSI-MSI fusion.The methods based on tensor networks,such as Tensor Train(TT)decomposition and Tensor Ring(TR)decomposition,have stronger ability to mine the internal structure of data than other techniques.In addition,in recent years,some researchers have explored the potential properties of tensor ring factors.These methods have achieved satisfactory results,but with two problems remain.Firstly,these models expand the factors into mode-n matrix,ignoring the correlation between different modes;Secondly,the matrix nuclear norm constraint attempts to model the tensor in the vector space based on matrix Singular Value Decomposition(SVD),and its representation capacity will be lost.Tensor Nuclear Norm(TNN)based on t-SVD(tensor singular value decomposition)can effectively maintain the inherent low-rank structure of tensor and avoid the loss of original information in the process of tensor matricization.Besides,the larger singular value in the image usually corresponds to the more important information,such as contours,sharp edges and smooth regions.However,TNN treats each singular value equally,which means that the larger singular value will be punished greatly and will suffer from the loss of the more important information and lead to suboptimal solution in practical applications.Therefore,aiming at the problem of HSI-MSI fusion,a low-rank tensor ring decomposition based on nonconvex tensor rank constraint is proposed.Specifically,the intrinsic low-rank structure of hyperspectral images is mined by directly applying the nonconvex tensor nuclear norm constraint based on t-SVD.Firstly,HSI is projected into a low dimensional compact space by using the global spectral low-rank of the hyperspectral image.Then,following the spatial nonlocal similarity,the reduced image is divided into multiple patches,and the similar ones are gathered one by one to form several three-dimensional tensor groups.Furthermore,the tensor ring decomposition technique is used to mine its internal low-rank structure and explore the essential characteristics of tensor ring factors.Different from the way that expands the factors into matrices and applies the nuclear norm constraint,this paper proposes to directly apply the nonconvex tensor nuclear norm on each factor,which fully exploits the inherent tensor structure and effectively avoids the loss of spatial-spectral correlation.In addition,this paper introduces log-function instead of l1norm to avoid excessive punishment of large singular values.Extensive experimental results show that the proposed method effectively improves the quality of the restored image.Compared with the latest fusion methods,the algorithm has better performance in quantitative evaluation and visual comparison.