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J. Eur. Opt. Society-Rapid Publ. 21, 31( 2025)
Independent Component Analysis( ICA), and their variants. PCA eliminates the correlation between different bands and identifies a linear combination of the original bands that maximizes the variance in pixel values. Essentially, it orders the transformed data by variance, ensuring that each principal component contains more information than subsequent components [ 8 ]. When the observed variables or spectral signals contain additive independent Gaussian noise, PCA can serve as an effective noise filtering method and may perform exceptionally well. Segmented PCA divides the data into several parts and processes them separately, retaining a certain amount of spatial information based on the principles of PCA [ 9 ]. ICA focuses on additive separable components, aiming to decompose multivariate signals into statistically independent non-Gaussian signals. This allows ICA to effectively separate mixed signals [ 10 ]. The use of higher-order statistical moments in ICA provides an advantage in mitigating the impact of noise and other interferences on spectral features [ 11 ]. Non-negative Matrix Factorization( NMF) reduces dimensionality by decomposing hyperspectral images into two non-negative matrices [ 12 ]. The non-negative constraint of NMF helps preserve critical spectral information while offering higher computational efficiency compared to PCA [ 13 ]. MNF arranges components based on image quality, with the noise ratio being the primary parameter used to describe image quality in this method [ 14 ]. Segmented MNF preserves unique spectral information within each segment, making it more efficient and valuable than standard MNF [ 15 ]. Band combination methods reduce the dimensionality of hyperspectral images by recombining band groups within specific spectral ranges or non-adjacent bands. Common band grouping techniques include Band Grouping Uniformly( BGU) [ 16 ] and Band Grouping by Spectral Correlation Coefficient( BGCC) [ 17 ]. Correlation grouping identifies bands with similar spectral characteristics by calculating the correlation coefficient between adjacent bands. K-means clustering, a simple hard clustering algorithm, iteratively optimizes cluster centers by minimizing intra-class distances to form fixed clustering results [ 18, 19 ]. Sparse-based clustering assumes that each pixel in a hyperspectral image can be represented by an atom in a dictionary, leveraging sparsity coefficients for band selection. Representative methods include sparse subspace clustering [ 20, 21 ]. The geometric structure of hyperspectral images in high-dimensional space often exhibits strong regularity, meaning the data tends to lie near a low-dimensional manifold [ 22 ]. Many researchers employ manifold learning to reduce dimensionality while preserving the intrinsic geometric structure and local neighborhood relationships of the data. Isometric Feature Mapping( ISOMAP) achieves dimensionality reduction by calculating the shortest path distance between data points along the manifold surface [ 23 ]. Locally Linear Embedding( LLE) preserves the local structure of data through local linear combinations [ 24 ]. Weighted Spatial-Spectral Combined Preserving Embedding( WSCPE) uses weighted mean filtering to eliminate noise and background interference, followed by fusing spatial-spectral information for manifold reconstruction [ 25 ]. In recent years, deep learning algorithms have gained widespread application in hyperspectral image processing. Variants of autoencoders, such as stacked autoencoders [ 26 ] and sparse autoencoders [ 27 ], utilize reconstruction principles to reduce the dimensionality of hyperspectral images. Generative Adversarial Networks( GANs) learn deep features of data through adversarial training of generators and discriminators, thereby achieving dimensionality reduction [ 28 ]. However, complex network structures can lead to overfitting, susceptibility to local minima, and high computational complexity [ 29 ]. Previous studies have primarily focused on dimensionality reduction itself, often neglecting the degree to which spatial and spectral information is preserved after dimensionality reduction and its subsequent impact on downstream tasks.
In this letter, we propose a dimensionality reduction method based on spatial-spectral preservation and MNF, aiming to preserve the spatial-spectral structure of the image while performing denoising and dimensionality reduction. The method in this article is divided into two parts. The first step is to use a transformation matrix to maximize the signal-to-noise ratio and image structural similarity while preserving the spatial information of the image to the greatest extent possible. The second step is to use a component selection strategy to select the optimal component group after transformation. Select a strategy to calculate the average change in the relative position of all pixels in the feature space. Use the component group closest to the spectral relative position before transformation as the final dimensionality reduction result.
2 The method
2.1 MNF for maintaining spatial structure
Observing hyperspectral images described as X ¼ HðSÞ ¼ ½ x 1; x 2;... x p Š T 2 R pn, where S 2 R pn is the noise-free hyperspectral image, p is the number of bands, and n is the number of pixels per band. X is transformed by matrix A 2 R pp to obtain:
2 3 2 z T 1 a T 1 z T X
3
2 a T 2 X
Z ¼ AX ¼ 6
. ¼
4
7.
: ð1Þ
6 5 4
7 5 a T p X z T p
The signal-to-noise ratio of z 1 2 R p is defined as:
f ¼ l � z2 1 varðn 1 Þ ¼ zT 1 z 1 = n ð2Þ varða T 1 NÞ
� Where l z 2
1 is the mean square of all pixel values in z1, n 1 is the noise vector of z 1, var( n 1) is the variance of noise in z 1, andN ¼ HðSÞ�S.
The average structural difference between z 1 and X can be characterized by Structural Similarity Index Measure( SSIM) as: