J. Eur. Opt. Society-Rapid Publ. 21, 31( 2025) 7
7. Jungle: Taken on April 6, 2024, with geographic coordinates( 38 ° 27 0 W, 114 ° 30 0 E) and a ground spatial resolution of 3.3 mm, all belong to the close-range jungle background. The hyperspectral image size is 1000 1000 89. Fake turf-B was placed in the Jungle.
3.2 Evaluation metrics
This section mainly introduces how to evaluate the degree of spatial information preservation before and after dimensionality reduction of hyperspectral data, and its impact on object detection tasks. Evaluating the degree of preservation of spatial information before and after dimensionality reduction is equivalent to assessing their spatial structural differences. In this paper, Structure Similarity Index Measure( SSIM), Peak Signal to Noise Ratio( PSNR), and Grey Level Co-occurrence Matrix( GLCM) are used for evaluation. Average the two hyperspectral images before and after dimensionality reduction along the spectral dimension to obtain X; Z 2 R mn, and the SSIM calculation equation between them is
SSIMðX; ZÞ ¼
4 XZcovðX; ZÞ ðX 2 þ Z 2 Þ ½ varðXÞþvarðZÞŠ: ð18Þ
SSIM can evaluate the brightness, contrast, and structural differences between two images. It is a perceptual model that is more in line with the intuitive perception of the human eye. The larger the value of SSIM, the more similar the two images are.
PSNR is often used in the field of image compression to evaluate the quality of signal reconstruction, which can characterize the error between corresponding pixels in two images. The larger its value, the more similar the two images are, and its calculation equation is
MAX
PSNRðX; ZÞ ¼ 20log 10 pffiffiffiffiffiffiffiffiffiffi: ð19Þ
MSE
Among them, MAX = max( X), MSEðX; ZÞ ¼ 1 mn
X m�1 X n�1
i¼0 j¼0
½ Xði; jÞ�Zði; jÞŠ 2.
Applying GLCM to evaluate the similarity between two images requires separately calculating the feature quantities of the images. The GLCM of a single image is obtained by the following equation:
Gi ð; jÞ ¼ Xm x¼l
X n
y¼l d ½ Xði; jÞ ¼ iŠd ½ Xðx 0; y 0 Þ ¼ jŠ: ð20Þ
Among them,( x 0, y 0)=( x + d cosh, y + d sinh), d is the distance, h is the direction. d is the indicator function, and if the condition holds, it is 1; otherwise, it is 0.
The feature quantities of the gray level co-occurrence matrix G are
Contrast ¼ X ði � jÞ 2 Gði; jÞ; ð21Þ i; j
P � ði � l i Þ j � l j Gði; jÞ i; j
Correlation ¼: ð22Þ r i r j
The closer the feature quantity is, the more similar the spatial structure of the image before and after dimensionality reduction. SSIM and PSNR are suitable for evaluating the overall similarity of images. SSIM conforms to human visual perception, while PSNR is used to quantify pixel level differences. GLCM is suitable for texture analysis and can reflect local texture feature differences in images.
The effect of dimensionality reduction can also be demonstrated by downstream object detection tasks. Hyperspectral target detection results are divided into objective and subjective analysis. Subjective analysis mainly involves decision-makers visualizing the detection results by combining ground-truth maps. Objective analysis uses receiver operating characteristic( ROC) and area under the curve( AUC). The ROC curve establishes the correlation between false alarm probability( PFA) and detection probability( PD) based on a common threshold s. The traditional two-dimensional ROC curve mainly comprises the s – PFA relationship curve and the s – PD relationship curve. The definitions of PD and PFA are as follows:
PD ¼ N d
N t
;
FPA ¼ N f
N b
: ð23Þ
Where N d is the number of real target pixels detected, which is the number of pixels that belong to the target and are considered the target by the detector, N t represents the total number of target pixels in the image. N f represents the number of detected false alarm pixels that belong to the background but are considered targets by the detector. N b represents the total number of background pixels in the image.
AUC quantitatively describes the degree of deviation of the ROC curve from the upper left corner. The values are as follows:
AUC ¼
Z 1
0
ROCðxÞdx: ð24Þ
The greater the offset of the ROC curve to the upper left, the larger the area below the curve line and the larger the AUC, indicating better detection performance. The flatter the ROC curve, the smaller the area below the curve, and the smaller the AUC, the worse the detection effect.
3.3 Parameter sensitivity analysis
Acquiring an accurate noise covariance matrix is a critical task, as its precision directly impacts the performance of the proposed method. Common approaches for estimating the noise covariance matrix include the median filtering method [ 30 ], spectral and spatial de-correlation( SSDC) method [ 31 ], HySime method [ 32 ], and Per-Pixel method [ 33 ]. These methods provide pixel-by-pixel noise estimation for hyperspectral data and facilitate the calculation of the noise covariance matrix. This section investigates the performance differences of the proposed method when using four distinct noise matrices as inputs and evaluates the role