Since the dimensionality of hyperspectral images is much higher than that of RGB images, it is time-consuming to extract gradient features and other operations directly from hyperspectral images. Therefore, the information of the low, middle and high frequency bands of the hyperspectral data is extracted to form a pseudo-colour image to simulate an RGB image, which is used to extract the colour and gradient information of the object. Assuming that the high light spectral data exists in 1 , 2 , ⋯ , p spectral bands. The lowest, middle and highest frequencies 1 , p / 2 , p are taken as sampling frequencies and cascaded to form a three-channel pseudo-colour image. The resulting pseudo-colour image is shown in Figure 1. The pseudo-colour image is shown in Figure 2.

Principal Component Analysis (PCA) is an effective method for reducing the dimensionality of hyperspectral image data. By performing PCA, the principal components effectively preserve the majority of the original data’s essential information. By leveraging PCA, a small amount of information is sacrificed in exchange for obtaining low-dimensional data from hyperspectral images. This trade-off enhances the efficiency of image fusion and denoising without compromising accuracy. Figure 3 provides a visual representation of the image fusion denoising process based on principal component analysis.

The inspiration for this article is derived from the advancements in weighted kernel paradigm minimization for color image noise removal methods. The principal concept of hyper-spectral image denoising based on PCA and BM3D, can be summarized as follows:

Find a set of orthogonal vectors in the measurement space that maximises the variance of the data according to the K-L transform, and project the original vector from the original n-dimensional space onto the m m ≪ n dimensional subspace formed by this set of orthogonal vectors. Its projected coefficients form a new eigenvector, completing the dimensional compression.

Let X ¯ = x ¯ 1 , x ¯ 1 , ⋯ , x ¯ p , X ¯ = 1 N ∑ j = 1 N x i j be the mean values of the vectors, while A = μ 1 , μ 2 , ⋯ μ d is composed of eigenvectors μ i corresponding to the eigenvalues λ i of the covariance matrix ∑ x = E X − X ¯ X − X ¯ T of X arranged from largest to smallest. Its PCA reconfiguration is shown in Eq. 1: X * = A Y (1)

After PCA transformation, the correlation between the individual vectors of Y is basically eliminated, and the first principal component contains the vast majority of the information in the original X , while the secondary principal components are dominated by noise. Therefore, the appropriate principal components can be selected for optimal linear reconstruction in the least squares sense, with reconstruction mean square error E M S = ∑ i = k + 1 d λ i . For the noise-containing X , the reconstruction error primarily consists of noise, and a certain degree of inter-spectral noise can be effectively removed. In the case of hyperspectral images, the noise, predominantly Gaussian white noise [8], is randomly distributed across multiple bands. The PCA process leverages inter-spectral correlation to partially mitigate inter-spectral noise and achieve dimensionality reduction. Meanwhile, BM3D targets the removal of intra-spectral noise by considering spatial domain correlations within the image. These two methods address the removal of noise in two dimensions by considering inter-spectral and intra-spectral similarities, respectively. The main flowchart of the algorithm is shown in Figure 4.

The fundamental principle of the PCA-based hyperspectral image fusion method is as follows:

The high-resolution panchromatic image is histogram-matched with the first principal component (PC1) influence after PCA transformation. This ensures that the panchromatic image has the same variance and grey-scale mean value as PC1. Subsequently, the histogram-matched panchromatic influence replaces the first principal component. The remaining principal components (PC2 to PCn) after noise removal are PCA inverted and fused with the panchromatic image to restore it to the original color space. This process results in the generation of a fused high-resolution image [9–12]. The transformation formula is shown in Eq. 2: Y = K X (2)

Where X is the pixel vector of the original hyperspectral image before PCA transformation, Y is the pixel vector of the component image after PCA transformation, and K is the transformation matrix, which is the transpose matrix of the eigenvector matrix S x of the X -space covariance matrix, as shown in Eq. 3: y 1 y 2 ⋮ y i ⋮ y n = k 11 k 21 ⋮ k n 1 k 12 k 22 ⋮ k n 2 ⋯ ⋯ k i j ⋯ k 1 n k 2 n ⋮ k n n × x 1 x 2 ⋮ x i ⋮ x n (3)

The role of K is to give weighting coefficients to the brightness of the image elements in multiple bands to achieve a multidimensional orthogonal linear variation, i.e., y 1 , y 2 , ⋯ , y n is x 1 , x 2 , ⋯ , x n is obtained by undergoing a linear transformation. When subjected to a linear transformation of the above form, the covariance matrix corresponding to Y is shown in Eq. 4: S y = K S x K T = λ 1     0   λ 2         ⋯   0     λ n (4) where λ 1 , λ 2 , ⋯ , λ n is the eigenvector value of the original hyperspectral image covariance matrix S x in order of its magnitude λ 1 > λ 2 > ⋯ > λ n .

The impact of the PCA-based denoising fusion algorithm on hyperspectral images is depicted in Figure 5.

In these figures, Figure 5C, obtained through PCA fusion of panchromatic and hyperspectral images, which not only retains high spatial resolution information but also maintains the spatial and spectral information of the image.

The YOLOv5 network structure illustrated in Figure 6, is composed of four main segments: Input, Backbone, Neck, and Prediction. Input involves data augmentation and Mosaic data enhancement, as well as adaptive anchor frame calculation and image scaling to optimize the performance of the neural network model. Acquiring a large volume of data is typically necessary for a neural network to function effectively, yet the process of obtaining new data often demands substantial time and labor costs [13]. Data augmentation techniques enable computers to efficiently generate data and expand the dataset, utilizing methods such as scaling, panning, rotation, and color transformations. Data augmentation offers the advantage of increasing the number of training samples and improving the model’s generalization power by incorporating relevant noise data.

In addition to fundamental data augmentation methods, YOLOv5 also incorporates the Mosaic data enhancement technique. This approach involves randomly cropping and scaling four images, and then it arranges and stitches them together to form a single picture. This method enriches the dataset while augmenting small sample targets and improving the network’s training speed. In normalization operations, the model’s memory requirement is reduced as the data from four images is calculated simultaneously [14–17].

Comparatively, YOLOv3 and YOLOv4 lack the ‘Backbone in Focus’ structure, with a more critical emphasis on the slicing operation. This operation allows a 4 * 4 * 3 image to be sliced into 2 * 2 * 12 feature maps. While the neck structure in YOLOv4 employs typical convolution operations, YOLOv5 incorporates the CSP2 structure borrowed from CSPnet to enhance network feature fusion.

Regarding the prediction output layer, YOLOv5 shares the anchor frame mechanism with YOLOv3 and v4. However, the main improvement lies in the development of the CIOU_Loss and the shift to DIOU_nms for prediction frame filtering. This modification facilitates detection of originally occluded or overlapped targets.

The KCF target tracking algorithm is a method based on kernel correlation filtering, belonging to the category of discriminative tracking [18]. It involves collecting a substantial number of positive and negative samples by populating the target frame in the initial tracking frame, resulting in a filled frame. The filled frame is cyclically shifted in the subsequent frame to generate a cyclic matrix. This process entails designating the region containing the target as positive samples and the remaining regions as negative samples. Subsequently, the target detector is trained by using these positive and negative samples, and then employed to detect whether the predicted position corresponds to the target’s location. The trained target detector is then utilized in the subsequent frame to ascertain the presence of the target. The filled frame from the previous frame is used to continue the cyclic shift in order to reclassify the images in the sample frames as positive and negative samples. The strongest response among these sample frames is selected as the filled frame of the target in the current frame. The samples acquired in the current frame are utilized to update the target detection classifier. Throughout this process, the ability to diagonalize the cyclic matrix in Fourier space and the application of Fast Fourier Transform (FFT) are leveraged to adapt the target detection classifier. These techniques are utilized to compute these samples, thereby improving operational speed. Firstly let a set of training samples as x i , y i , x i is the sample labels, then the regression function is f x i = w T x i , w is the column vector denoting the weight coefficients, which can be solved by the least squares method to solve the solution [19], which is expressed in Eq. 5 as follows: min w ∑ i f x i − y i 2 + λ w 2 (5)

Where λ is the regularisation function for the structural complexity of the control system.

By introducing a nonlinear mapping function Φ x i , the low-dimensional nonlinearly indivisible problem can be mapped to a high-dimensional space and thus transformed into a linear solution, as shown in Eq. 6: w = ∑ i a i ϕ x i (6)

Substituting Eq. 6 into Eq. 5 under the kernel space and performing a discrete Fourier variation is shown in Eq. 7: α ∧ = y ∧ k x x ∧ + λ (7)

At this point, the problem of optimisation problem for w is transformed into a problem of solving for a, where Eq. α ∧ is the discrete Fourier variation of α , k x x ∧ is the first row element of the kernel function matrix.

After getting the nonlinear filter, the images in the video image block image block is detected to find out the location of the target. The image block to be detected is denoted by z . The output response equation of the detection process is shown in Equation 8: f z = K z T α (8)

Where K z denotes the kernel matrix between the training samples and the candidate samples, which is an asymmetric matrix, and each element of K z is defined as K i j z = K P i − 1 z , P j − 1 x , where P undisplaced matrix, which serves to realise the displacements. The model of the associated filter is initialised based on the features of the UAV selected in the frame of the initial frame; secondly, the template is used to find the position with the largest response in the captured frames in the subsequent frames, which serves as the position of the UAV that is tracked in the current frame; and lastly, the filter is updated using the position of the UAV device determined in each frame.

The working block diagram of the original KCF tracking algorithm in the process of visually tracking a UAV is shown in Figure 7.

The DSST multi-scale filter accomplishes target tracking by leveraging the correlation filtering principle, effectively addressing changes in the target’s scale. It employs scale filters and position filters to represent the scale variation of the target, thereby delivering precise positional information. Through the utilization of the scale filter, the model’s outcomes can be fine-tuned at a specific location to attain the optimal scale response, thereby achieving the intended objective.

(1) The correlation operation values of the position filter h and the feature matrix block are constructed, and then the error function ε between it and the expected value g is calculated.

Firstly, the input image I is analysed to find a centroid and compare it with the original tracking region to determine the best sample value. Then, by analysing the features in the d -dimension of each pixel point of the extracted sample, information about its original grey value (1-dimensional) and HOG features ( 1 − d -dimensional) can be obtained. Eq. 9 is the expression of the error function. Where f denotes the matrix block extracted from the feature map extracted from the feature map, f 1 denotes the matrix block corresponding to the l th dimensional feature, = 1 , 2 , ⋯ , d . h 1 denotes the l th dimensional vector in the filter corresponding to f 1 , h = h l , ⋯ , h d . g denotes the desired result of the correlation calculation between the eigenvalue matrix block constructed from the 2D Gaussian function and the filter. Where the regular term coefficients, λ are usually used to adjust the parameters to avoid zero-component cases during the frequency domain conversion [20]. ε = ∑ l = 1 d h l × f l − g 2 + λ ∑ l = 1 d h l 2 (9)

(2) By using discrete Fourier transform and Parseval’s theorem, the value of the error function under least square is calculated. as shown in Equation 10:

In the above equation, H, A, B, G, F denote the discrete Fourier transform of the corresponding function, and the variables with horizontal lines are denoted as conjugate complex numbers. A t l , B t l , denote the numerator and denominator of the filter value at frame time. In order to simplify the solution, Eq. 11 is the approximate solution formula of A t l , B t l : A t l = 1 − η A t − 1 l + η G ¯ t F t l B t l = 1 − η B t − 1 + η ∑ k − 1 d F ¯ t k F t k (11)

(3) Using the position filter parameters at frame t , the correlation score y of the image feature matrix block z with the known filter is computed by A t l , B t l when predicting the next frame in the video. The specific process is denoted as follows:

Where the position corresponding to the maximum value of y is the centre point p t + 1 of the tracked target in the predicted t + 1 frame.

(4) Construct and solve the scale filter h s c a l e

It is known that at frame t , the position p t in image I t represents the centre point of the outer rectangle of the tracked target, and the minimum size of the outer rectangular region of the tracked target is P × R .Firstly, centred on p t , intercept M samples J n at different scales according to Equation 13: J n = a n P × a n × R , n ∈ − S − 1 2 , ⋯ S − 1 2 (13)

Then by extracting the features of sample J n as f = f l , ⋯ , f n , Finally, the scale filter h s c a l e is obtained through Eq. 11.

(1) Predict the scale of the tracked target for frame t + 1 .

To predict the centre of the tracked target position p t + 1 for frame t + 1 with the position filter, and extracting multi-scale samples z s c a l e , solve for the scale according to Equation 12: The scale of the sample corresponding to the maximum value of score y is the scale S t + 1 of the prediction.

(2) Based on the predicted tracking target position p t + 1 at frame t + 1 with scale S t + 1 , Update the position according to Eqs 9–11 with the parameters of the scale filter to start the next iteration.

A combined scheme of the YOLOv5 algorithm and the KCF algorithm is proposed to leverage the advantages of both methods. In this proposed approach, the real-time shooting frame utilizes the YOLOv5 algorithm for visual target detection, determining the position of the tracked UAV in the current frame. This result serves as the initial frame for the subsequent tracking in the KCF algorithm. Additionally, the scale estimation filtering algorithm from the DSST algorithm is integrated into the KCF tracking algorithm to enable real-time detection and tracking of the UAV. The specific flow of this combined approach is illustrated in Figure 8.

The flow of the hyperspectral low altitude UAV target tracking algorithm, based on deep learning and improved KCF tracking depicted in Figure 8, is as follows:

Firstly, a hyperspectral camera is utilized to acquire the UAV image sequence. Simultaneously, the YOLOv5 algorithm assesses whether the confidence level exceeds a predetermined threshold. If the threshold is reached, it indicates a successful detection, and the current frame of the hyperspectral image is then transmitted to the KCF tracking algorithm. Following the determination of the target’s position during the tracking of subsequent frames, the DSST algorithm is employed to determine the size of the target frame for each frame. It evaluates the correctness of the tracking based on the corresponding peak value of each frame. If the tracking is determined to be correct, commands are issued to continue the tracking, and in the event of failure, a return to the YOLOv5 algorithm is initiated to conduct additional target detection until the completion of the tracking process. This is done so that when the UAV experiences occlusion, lighting changes, and rapid movement resulting in the loss of the target in the image sequence, the current frame can be skipped and stepped to the target reappearance frame. Hyperspectral image sequences are chosen to reduce the interference of background factors and improve the efficiency of target recognition.