Compressive Hyperspectral Imaging via Sparse Tensor and Nonlinear Compressed Sensing

Yang, Shuyuan; Wang, Min; Peng, Li; Li, Jin; Wu, Bin; Jiao, Licheng

doi:10.1109/tgrs.2015.2429146

Cited by 79 publications

(36 citation statements)

References 63 publications

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“…, ξ K Q˘i s an order-3 diagonal tensor with Ξ i,i,i " ξ i . Problem (21) can be solved using an alternating least-squares strategy [17]. Finally, the solution…”

Section: Solving With Respect To Pmentioning

confidence: 99%

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Imbiriba

Borsoi

Bermudez

2020

IEEE Trans. Geosci. Remote Sensing

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Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these missmodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember variability through generalizations of the mixing model, the success of these techniques depend on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of hyperspectral images as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems . These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios; and 2) they lack guarantees that endmembers and abundances will be correctly factorized in their respective tensors. In this work, we propose a more flexible approach, called ULTRA-V, that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability.

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“…, ξ K Q˘i s an order-3 diagonal tensor with Ξ i,i,i " ξ i . Problem (21) can be solved using an alternating least-squares strategy [17]. Finally, the solution…”

Section: Solving With Respect To Pmentioning

confidence: 99%

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Imbiriba

Borsoi

Bermudez

2020

IEEE Trans. Geosci. Remote Sensing

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“…Given an Nth-order tensor T ∈ R I 1 ×I 2 ×···×I N , the n-mode unfolding vector of tensor T is obtained by fixing every index except the one in the mode n [26]. The n-mode unfolding matrix is defined by arranging all of the n-mode vectors as columns of a matrix, i.e., the n-mode unfolding matrix…”

Section: Tensor Notations and Preliminariesmentioning

confidence: 99%

Tensor-Based Sparse Representation Classification for Urban Airborne LiDAR Points

Pfeifer

Liu

2017

Remote Sensing

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Abstract:The common statistical methods for supervised classification usually require a large amount of training data to achieve reasonable results, which is time consuming and inefficient. In many methods, only the features of each point are used, regardless of their spatial distribution within a certain neighborhood. This paper proposes a tensor-based sparse representation classification (TSRC) method for airborne LiDAR (Light Detection and Ranging) points. To keep features arranged in their spatial arrangement, each LiDAR point is represented as a 4th-order tensor. Then, TSRC is performed for point classification based on the 4th-order tensors. Firstly, a structured and discriminative dictionary set is learned by using only a few training samples. Subsequently, for classifying a new point, the sparse tensor is calculated based on the tensor OMP (Orthogonal Matching Pursuit) algorithm. The test tensor data is approximated by sub-dictionary set and its corresponding subset of sparse tensor for each class. The point label is determined by the minimal reconstruction residuals. Experiments are carried out on eight real LiDAR point clouds whose result shows that objects can be distinguished by TSRC successfully. The overall accuracy of all the datasets is beyond 80% by TSRC. TSRC also shows a good improvement on LiDAR points classification when compared with other common classifiers.

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“…In merit of the tensor algebra, one can perform spectral-spatial classification by treating the HSI as a whole entity. Interested readers can consult [39,41,[49][50][51] for more details. Moreover, as shown in Figure 1, the original spatial structure is preserved by tensor, while the spatially connected constraint among local neighborhoods is lost in the vector representation.…”

Section: Tensor Notations and Preliminariesmentioning

confidence: 99%

“…3-D gray-level co-occurrence [40] is presented to extract discriminant co-occurrence features for better classification accuracy. A compressive hyperspectral imaging method based on sparse tensors and nonlinear compressed sensing is proposed in [41]. Moreover, a local tensor discriminative analysis technique (LTDA) [42] is presented to integrate spectral-spatial features and tensor discriminant analysis for HSI classification.…”

Section: Introductionmentioning

confidence: 99%

Tensor Block-Sparsity Based Representation for Spectral-Spatial Hyperspectral Image Classification

Liu

2016

Remote Sensing

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Abstract:Recently, sparse representation has yielded successful results in hyperspectral image (HSI) classification. In the sparse representation-based classifiers (SRCs), a more discriminative representation that preserves the spectral-spatial information can be exploited by treating the HSI as a whole entity. Based on this observation, a tensor block-sparsity based representation method is proposed for spectral-spatial classification of HSI in this paper. Unlike traditional vector/matrix-based SRCs, the proposed method consists of tensor block-sparsity based dictionary learning and class-dependent block sparse representation. By naturally regarding the HSI cube as a third-order tensor, small local patches centered at the training samples are extracted from the HSI to maintain the structural information. All the patches are then partitioned into a number of groups, on which a dictionary learning model is constructed with a tensor block-sparsity constraint. A test sample is also expressed as a small local patch and the block sparse representation is then performed in a class-wise manner to take advantage of the class label information. Finally, the category of the test sample is determined by using the minimal residual. Experimental results of two real-world HSIs show that our proposed method greatly improves the classification performance of SRC.

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Compressive Hyperspectral Imaging via Sparse Tensor and Nonlinear Compressed Sensing

Cited by 79 publications

References 63 publications

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Tensor-Based Sparse Representation Classification for Urban Airborne LiDAR Points

Tensor Block-Sparsity Based Representation for Spectral-Spatial Hyperspectral Image Classification

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