CN-122024039-A - Hyperspectral image unmixing method based on spatial structure retention double-end-element-set non-negative tensor decomposition

CN122024039ACN 122024039 ACN122024039 ACN 122024039ACN-122024039-A

Abstract

The invention discloses a hyperspectral image unmixing method based on double-end-set non-negative tensor decomposition maintained by a spatial structure, and belongs to the technical field of hyperspectral remote sensing image analysis. The method mainly comprises the steps of approximately representing hyperspectral image data as the product of an end member matrix and an abundance matrix, adding a noise tensor, introducing a self-adaptive Sobel weighted spatial regularization term to the abundance matrix under the condition of fixing the end member matrix, carrying out iterative updating on the abundance matrix through gradient weighting coefficients in the horizontal and vertical directions, introducing a truncated low-rank sparse constraint to the decomposed end member matrix under the condition of fixing the abundance matrix, and carrying out alternate optimization updating on a pure end member matrix and a variant component matrix respectively by adopting an iterative re-weighting strategy. The invention can separate the pure part and the variant part of the end member while maintaining the continuity of the space structure in the unmixing, thereby improving the spectral purity, the physical interpretability and the noise immunity of the unmixing result.

Inventors

YU CHUNYAN
YIN XUEER
SONG MEIPING

Assignees

大连海事大学

Dates

Publication Date: 20260512
Application Date: 20251230

Claims (6)

1. A method for unmixing a hyperspectral image based on a spatial structure-preserving two-terminal set non-negative tensor decomposition, comprising the steps of: s1, acquiring hyperspectral data to be unmixed, and representing the hyperspectral data to be unmixed as a three-dimensional non-negative tensor; S2, initializing an end member matrix and an abundance matrix, and establishing a non-negative tensor decomposition model, so that the hyperspectral image data is approximately expressed as the product of the end member matrix and the abundance matrix and then added with a noise tensor; S3, under the condition of fixed end member matrix, introducing a self-adaptive Sobel weighted spatial regularization term to the abundance matrix, and iteratively updating the abundance matrix through gradient weighting coefficients in the horizontal and vertical directions; s4, under the condition of fixing an abundance matrix, decomposing the end member matrix into the sum of a pure end member matrix and a variation component matrix, introducing a truncated low-rank sparse constraint to the decomposed end member matrix, and adopting an iterative re-weighting strategy to alternately optimize and update the pure end member matrix and the variation component matrix respectively; And S5, repeatedly executing the step S3 and the step S4 until convergence conditions are met, and obtaining a final end member matrix and an abundance matrix to realize unmixing of the hyperspectral image.
2. A method of unmixing hyperspectral images based on spatial structure preserving two-terminal set non-negative tensor decomposition according to claim 1 characterized in that the hyperspectral data to be unmixed is represented as: Wherein, the A data cube representing hyperspectral data, Represents the number of pixels and, The number of spectral bands is represented, Is an abundance plot of the r-th end member, approximately composed of two low rank matrices And The representation is made of a combination of a first and a second color, Is the (r) th end member, and the (c) th end member, The tensor of the noise is represented by, The minimum reconstruction error for constructing hyperspectral data is: Wherein the method comprises the steps of Is a matrix of all-ones, Is a balance parameter for balancing the sum of reconstruction errors and is a constraint.
3. The hyperspectral image unmixing method based on the double-end-member-set non-negative tensor decomposition maintained by a spatial structure according to claim 2, wherein under the condition of fixing an end-member matrix, an adaptive Sobel weighted spatial regularization term is introduced for an abundance matrix, and the abundance matrix is iteratively updated by gradient weighting coefficients in horizontal and vertical directions, and the method comprises the following formula for calculating the adaptive Sobel weighting coefficients: Wherein, the Respectively representing horizontal and vertical gradient operators under the concept of Sobel filtering.
4. The method for unmixing hyperspectral images based on the two-terminal-set non-negative tensor decomposition maintained by a spatial structure according to claim 3, wherein under the condition of fixing the terminal-element matrix, an adaptive Sobel weighted spatial regularization term is introduced for the abundance matrix, and the abundance matrix is iteratively updated by gradient weighting coefficients in horizontal and vertical directions, comprising the following steps: Wherein, the Is regularized intensity coefficient, respectively controls Penalty weights of (2).
5. The method for unmixing hyperspectral image based on spatial structure-preserving double-end-member set non-negative tensor decomposition according to claim 4, wherein under the condition of fixed abundance matrix, decomposing the end-member matrix into the sum of pure end-member matrix and variant component matrix, introducing truncated low-rank-sparse constraint to the decomposed end-member matrix, and respectively carrying out alternate optimization updating on the pure end-member matrix and variant component matrix by adopting iterative re-weighting strategy, comprising the following steps: Wherein, the Is a matrix of real end-members, Is a matrix of pure end members, Is the r-th pure end member matrix, Is a matrix of variant components, Is the r variation component matrix, the size is all Wherein Is the number of the end members, and the number of the end members, Is the band number, p is the weighting parameter, w is the weighting factor corresponding to the singular value σ, S p is the applied Schatten-p norm, λ represents the sparse regularization parameter.
6. The method for unmixing hyperspectral image based on spatial structure preserving double-end-member set non-negative tensor decomposition according to claim 5, wherein under the condition of fixed abundance matrix, decomposing the end-member matrix into the sum of pure end-member matrix and variant component matrix, introducing truncated low-rank-sparse constraint to the decomposed end-member matrix, and respectively carrying out alternate optimization updating on the pure end-member matrix and the variant component matrix by adopting iterative re-weighting strategy, further comprising optimizing the minimum reconstruction error of hyperspectral data as follows: Wherein, the Representing the penalty strength.

Description

Hyperspectral image unmixing method based on spatial structure retention double-end-element-set non-negative tensor decomposition Technical Field The invention relates to the field of hyperspectral remote sensing image analysis and signal processing, in particular to a hyperspectral image unmixing method based on double-end-element-set non-negative tensor decomposition maintained by a spatial structure. Background The hyperspectral imaging technology can realize fine distinction in spectrum dimension by collecting spectrum information of ground objects in hundreds of continuous wave bands, and is one of core technologies in ground object identification and precise remote sensing at present. However, due to spatial resolution and mixed pixel effects, a single pixel typically contains a mixed spectrum of multiple clutter materials, such that the problem of "mixed pixels" is prevalent in hyperspectral images. The traditional linear mixed model is difficult to simultaneously maintain the spectral purity and the spatial uniformity for the analysis of mixed pixels in a complex scene. In recent years, nonnegative tensor decomposition has been widely used for hyperspectral unmixing, and the interpretability of unmixing is significantly improved by performing end member and abundance decomposition under nonnegative constraints. However, the existing nonnegative tensor decomposition method generally does not fully utilize the spatial correlation between pixels in the modeling process and lacks an effective description mechanism for the variation of an end member spectrum along with the spatial variation, so that the defects that on one hand, the phenomenon of discontinuous abundance estimation or noise interference easily occurs in a homogeneous region and the spatial consistency of abundance distribution is reduced in the actual analysis process, and on the other hand, the end member spectrum distortion or abundance diffusion easily occurs in an end member boundary or a region with obvious spectrum variation, so that the end member boundary is fuzzy and the analysis precision is reduced, and the stability and the reliability of a hyperspectral unmixing result under a complex scene are influenced. Therefore, a new method for high-spectrum unmixing is needed, which can not only maintain the space structure, but also separate the pure end member and the variant end member, and realize the stable spectrum structure through low-rank constraint. Disclosure of Invention In view of the shortcomings of the prior art, the invention provides a hyperspectral image unmixing method based on double-end-set non-negative tensor decomposition maintained by a spatial structure. According to the invention, by introducing the spatial gradient constraint and the weighted low-rank constraint, the spatial structural continuity is maintained in the unmixing process, and meanwhile, the pure part and the variant part of the end member can be separated, so that the spectral purity, the physical interpretability and the noise immunity of the unmixing result are improved. The invention adopts the following technical means: A method for unmixing a hyperspectral image based on spatial structure-preserving two-terminal-set non-negative tensor decomposition, comprising the steps of: s1, acquiring hyperspectral data to be unmixed, and representing the hyperspectral data to be unmixed as a three-dimensional non-negative tensor; S2, initializing an end member matrix and an abundance matrix, and establishing a non-negative tensor decomposition model, so that the hyperspectral image data is approximately expressed as the product of the end member matrix and the abundance matrix and then added with a noise tensor; S3, under the condition of fixed end member matrix, introducing a self-adaptive Sobel weighted spatial regularization term to the abundance matrix, and iteratively updating the abundance matrix through gradient weighting coefficients in the horizontal and vertical directions; s4, under the condition of fixing an abundance matrix, decomposing the end member matrix into the sum of a pure end member matrix and a variation component matrix, introducing a truncated low-rank sparse constraint to the decomposed end member matrix, and adopting an iterative re-weighting strategy to alternately optimize and update the pure end member matrix and the variation component matrix respectively; And S5, repeatedly executing the step S3 and the step S4 until convergence conditions are met, and obtaining a final end member matrix and an abundance matrix to realize unmixing of the hyperspectral image. Further, the hyperspectral data to be unmixed is expressed as: Wherein, the A data cube representing hyperspectral data,Represents the number of pixels and,The number of spectral bands is represented,Is an abundance plot of the r-th end member, approximately composed of two low rank matricesAndThe representation is made of a combination of a first and a second color,