scholarly journals Sparse Constrained Low Tensor Rank Representation Framework for Hyperspectral Unmixing

2021 ◽  
Vol 13 (8) ◽  
pp. 1473
Author(s):  
Le Dong ◽  
Yuan Yuan
Keyword(s):  
Real Data ◽  
Low Rank ◽  
Tensor Rank ◽  
Data Sets ◽  
Local Similarity ◽  
Tensor Factorization ◽  
Similarity Group ◽  
Spatial Domains ◽  
Non Local ◽  
The Stability

Recently, non-negative tensor factorization (NTF) as a very powerful tool has attracted the attention of researchers. It is used in the unmixing of hyperspectral images (HSI) due to its excellent expression ability without any information loss when describing data. However, most of the existing unmixing methods based on NTF fail to fully explore the unique properties of data, for example, low rank, that exists in both the spectral and spatial domains. To explore this low-rank structure, in this paper we learn the different low-rank representations of HSI in the spectral, spatial and non-local similarity modes. Firstly, HSI is divided into many patches, and these patches are clustered multiple groups according to the similarity. Each similarity group can constitute a 4-D tensor, including two spatial modes, a spectral mode and a non-local similarity mode, which has strong low-rank properties. Secondly, a low-rank regularization with logarithmic function is designed and embedded in the NTF framework, which simulates the spatial, spectral and non-local similarity modes of these 4-D tensors. In addition, the sparsity of the abundance tensor is also integrated into the unmixing framework to improve the unmixing performance through the L2,1 norm. Experiments on three real data sets illustrate the stability and effectiveness of our algorithm compared with five state-of-the-art methods.

scholarly journals Non-Local Low-Rank Cube-Based Tensor Factorization for Spectral CT Reconstruction

2019 ◽  
Vol 38 (4) ◽  
pp. 1079-1093 ◽  
Author(s):  
Weiwen Wu ◽  
Fenglin Liu ◽  
Yanbo Zhang ◽  
Qian Wang ◽  
Hengyong Yu
Keyword(s):  
Low Rank ◽  
Tensor Factorization ◽  
Ct Reconstruction ◽  
Spectral Ct ◽  
Non Local

scholarly journals Tucker Tensor Analysis of Matérn Functions in Spatial Statistics

2019 ◽  
Vol 19 (1) ◽  
pp. 101-122 ◽  
Author(s):  
Alexander Litvinenko ◽  
David Keyes ◽  
Venera Khoromskaia ◽  
Boris N. Khoromskij ◽  
Hermann G. Matthies
Keyword(s):  
Covariance Matrix ◽  
Computing Time ◽  
Large Data ◽  
Three Dimensions ◽  
Low Rank ◽  
Tensor Rank ◽  
Data Sets ◽  
Storage Cost ◽  
Covariance Functions ◽  
Rank Tensor

AbstractIn this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will allow us to consider much larger data sets or finer meshes. Covariance matrices are crucial in spatio-temporal statistical tasks, but are often very expensive to compute and store, especially in three dimensions. Therefore, we approximate covariance functions by cheap surrogates in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matérn- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence. We prove the exponential convergence of the Tucker and canonical approximations in tensor rank parameters. Several statistical operations are performed in this low-rank tensor format, including evaluating the conditional covariance matrix, spatially averaged estimation variance, computing a quadratic form, determinant, trace, loglikelihood, inverse, and Cholesky decomposition of a large covariance matrix. Low-rank tensor approximations reduce the computing and storage costs essentially. For example, the storage cost is reduced from an exponential{\mathcal{O}(n^{d})}to a linear scaling{\mathcal{O}(drn)}, wheredis the spatial dimension,nis the number of mesh points in one direction, andris the tensor rank. Prerequisites for applicability of the proposed techniques are the assumptions that the data, locations, and measurements lie on a tensor (axes-parallel) grid and that the covariance function depends on a distance,{\|x-y\|}.

scholarly journals Superpixel Weighted Low-rank and Sparse Approximation for Hyperspectral Unmixing

2022 ◽  
Author(s):  
Taner Ince ◽  
Tugcan Dundar ◽  
Seydi Kacmaz ◽  
Hasari Karci
Keyword(s):  
Spatial Structure ◽  
Hyperspectral Image ◽  
Real Data ◽  
Approximation Problem ◽  
Sparse Approximation ◽  
Hyperspectral Data ◽  
Low Rank ◽  
Data Sets ◽  
Spatial Weight ◽  
Homogeneous Regions

We propose a superpixel weighted low-rank and sparse unmixing (SWLRSU) method for sparse unmixing. The proposed method consists of two steps. In the first step, we segment hyperspectral image into superpixels which are defined as the homogeneous regions with different shape and sizes according to the spatial structure. Then, an efficient method is proposed to obtain a spatial weight term using superpixels to capture the spatial structure of hyperspectral data. In the second step, we solve a superpixel guided low-rank and spatially weighted sparse approximation problem in which spatial weight term obtained in the first step is used as a weight term in sparsity promoting norm. This formulation exploits the spatial correlation of the pixels in the hyperspectral image efficiently, which yields satisfactory unmixing results. The experiments are conducted on simulated and real data sets to show the effectiveness of the proposed method.

Remote Sensing Image Reconstruction Method Based on Non-Local Similarity and Low Rank Matrix

2016 ◽  
Vol 36 (6) ◽  
pp. 0611002
Author(s):  
黄芝娟 Huang Zhijuan ◽  
唐超影 Tang Chaoying ◽  
陈跃庭 Chen Yueting ◽  
李奇 Li Qi ◽  
徐之海 Xu Zhihai ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Image Reconstruction ◽  
Remote Sensing Image ◽  
Low Rank ◽  
Reconstruction Method ◽  
Local Similarity ◽  
Rank Matrix ◽  
Image Reconstruction Method ◽  
Non Local ◽  
Low Rank Matrix

scholarly journals Stable Tensor Principal Component Pursuit: Error Bounds and Efficient Algorithms

Sensors ◽  
2019 ◽  
Vol 19 (23) ◽  
pp. 5335 ◽  
Author(s):  
Wei Fang ◽  
Dongxu Wei ◽  
Ran Zhang
Keyword(s):  
Error Bounds ◽  
Rapid Development ◽  
Principal Component ◽  
Real Data ◽  
Superior Performance ◽  
Sensor Technology ◽  
Data Sets ◽  
Tensor Factorization ◽  
Principal Component Pursuit ◽  
Tensor Data

The rapid development of sensor technology gives rise to the emergence of huge amounts of tensor (i.e., multi-dimensional array) data. For various reasons such as sensor failures and communication loss, the tensor data may be corrupted by not only small noises but also gross corruptions. This paper studies the Stable Tensor Principal Component Pursuit (STPCP) which aims to recover a tensor from its corrupted observations. Specifically, we propose a STPCP model based on the recently proposed tubal nuclear norm (TNN) which has shown superior performance in comparison with other tensor nuclear norms. Theoretically, we rigorously prove that under tensor incoherence conditions, the underlying tensor and the sparse corruption tensor can be stably recovered. Algorithmically, we first develop an ADMM algorithm and then accelerate it by designing a new algorithm based on orthogonal tensor factorization. The superiority and efficiency of the proposed algorithms is demonstrated through experiments on both synthetic and real data sets.

scholarly journals Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

2020 ◽  
Vol 14 (2) ◽  
pp. 339-361
Author(s):  
Weihong Guo ◽  
◽  
Wei Wan ◽  
Jun Liu ◽  
Haiyang Huang ◽  
...  
Keyword(s):  
Hyperspectral Image ◽  
Super Resolution ◽  
Low Rank ◽  
Tensor Factorization ◽  
Non Local ◽  
Image Super Resolution

scholarly journals Outlier-Robust Multi-Aspect Streaming Tensor Completion and Factorization

2019 ◽  
Author(s):  
Mehrnaz Najafi ◽  
Lifang He ◽  
Philip S. Yu
Keyword(s):  
Real World ◽  
Missing Values ◽  
Real Data ◽  
Low Rank ◽  
Tensor Factorization ◽  
Tensor Completion ◽  
Smooth Optimization ◽  
Novel Method ◽  
Real World Datasets ◽  
Tensor Data

With the increasing popularity of streaming tensor data such as videos and audios, tensor factorization and completion have attracted much attention recently in this area. Existing work usually assume that streaming tensors only grow in one mode. However, in many real-world scenarios, tensors may grow in multiple modes (or dimensions), i.e., multi-aspect streaming tensors. Standard streaming methods cannot directly handle this type of data elegantly. Moreover, due to inevitable system errors, data may be contaminated by outliers, which cause significant deviations from real data values and make such research particularly challenging. In this paper, we propose a novel method for Outlier-Robust Multi-Aspect Streaming Tensor Completion and Factorization (OR-MSTC), which is a technique capable of dealing with missing values and outliers in multi-aspect streaming tensor data. The key idea is to decompose the tensor structure into an underlying low-rank clean tensor and a structured-sparse error (outlier) tensor, along with a weighting tensor to mask missing data. We also develop an efficient algorithm to solve the non-convex and non-smooth optimization problem of OR-MSTC. Experimental results on various real-world datasets show the superiority of the proposed method over the baselines and its robustness against outliers.

scholarly journals Superpixel Weighted Low-rank and Sparse Approximation for Hyperspectral Unmixing

2022 ◽  
Author(s):  
Taner Ince ◽  
Tugcan Dundar ◽  
Seydi Kacmaz ◽  
Hasari Karci
Keyword(s):  
Spatial Structure ◽  
Hyperspectral Image ◽  
Real Data ◽  
Approximation Problem ◽  
Sparse Approximation ◽  
Hyperspectral Data ◽  
Low Rank ◽  
Data Sets ◽  
Spatial Weight ◽  
Homogeneous Regions

We propose a superpixel weighted low-rank and sparse unmixing (SWLRSU) method for sparse unmixing. The proposed method consists of two steps. In the first step, we segment hyperspectral image into superpixels which are defined as the homogeneous regions with different shape and sizes according to the spatial structure. Then, an efficient method is proposed to obtain a spatial weight term using superpixels to capture the spatial structure of hyperspectral data. In the second step, we solve a superpixel guided low-rank and spatially weighted sparse approximation problem in which spatial weight term obtained in the first step is used as a weight term in sparsity promoting norm. This formulation exploits the spatial correlation of the pixels in the hyperspectral image efficiently, which yields satisfactory unmixing results. The experiments are conducted on simulated and real data sets to show the effectiveness of the proposed method.

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