Research On Hyperspectral Image Classification Algorithm Based On Quaternion And Improved L₂ Regularizatio

Hyperspectral imaging is a three-dimensional image that contains spatial and spectral dimensions,providing rich spatial and spectral information.Based on this information,it can accurately identify and classify land objects,making hyperspectral imaging widely used in many fields such as ocean research,vegetation ecology,and mineral geology.However,this large amount of data brings challenges to hyperspectral image classification:the inter-band correlation of hyperspectral images leads to data redundancy and increased classification computing costs;high dimensionality,uncertainty,and heterogeneity make traditional classification models difficult to directly process original hyperspectral images;labeling category labels is difficult,model learning is insufficient,and sample types cannot be accurately estimated;spectral features may vary spatially,leading to"same spectrum different object"and"same object different spectrum"phenomena,weakening the algorithm’s classification ability.This paper discusses algorithms for feature extraction and classification of hyperspectral images based on quaternion theory and L₂ regularization theory to address these issues.This paper mainly studies how to enhance the classification accuracy of the algorithm and improve its discriminability and stability using L₂regularization.The main research work of this paper is as follows:（1）Proposing and establishing a quaternion-based hyperspectral image classification algorithm.Due to the high dimensionality and large data volume of hyperspectral data,this paper uses quaternion matrix representation of reduced data and uses quaternion Weber local descriptor histogram to extract deep spatial features of images,in order to solve the"same spectrum different object"and"same object different spectrum"problems.The specific experimental steps of this algorithm are as follows:firstly,the image is subjected to kernel principal components analysis（KPCA）for dimensionality reduction,and the hyperspectral image is represented by a quaternion matrix.Quaternions can maintain the spatial structure of the image and provide a unified algebraic structure for subsequent feature extraction.Then,in order to fully utilize the spatial position relationship between pixels,the quaternion Weber local descriptor is used to extract differential excitation features and gradient direction features,which alleviates spatial variability.Secondly,a double-scale feature histogram is constructed.Finally,the spectral features and spatial features extracted by the quaternion Weber local descriptor are fused for classification.This paper conducts experimental verification on three publicly available datasets using the above algorithm.Multi-scale residual attention algorithm（MAFN）,3D convolutional neural networks（3D-CNN）,spatial-spectral transformer fusion algorithm（SST-FA）,and residual-hybrid SN（R-Hybrid SN）are used as comparisons.According to the experimental results,the overall classification accuracy of this paper’s algorithm on the Indian Pines dataset was improved by 2.69%compared to MAFN algorithm and by 0.53%on the Pavia University Scene dataset compared to R-Hybrid SN algorithm,and 1.99%on the Salinas dataset compared to R-Hybrid SN algorithm,which demonstrates the classification performance of this algorithm.At the same time,the small variance exhibited by this algorithm also proves its effectiveness.（2）Proposing and establishing a collaborative representation classification algorithm based on improved L₂ regularization.In order to solve the problems of difficult labeling of category labels and insufficient model learning,and to avoid overfitting of the classification model,this paper introduces improved L₂ regularization and establishes a collaborative representation classification algorithm based on improved L₂ regularization.The specific experimental steps of this algorithm are as follows:initializing the hyperspectral image represented as a quaternion matrix after KPCA dimensionality reduction,establishing a sparse dictionary,introducing two regularization parameters,obtaining a unique closed-form solution by taking the derivative of the objective function,and ensuring the stability and uniqueness of the solution.Finally,the classification labels of the training samples are obtained.This paper conducts experimental verification on the Indian Pines dataset and the Pavia University Scene dataset,and uses sparse representation-based classification algorithm（SRC）,collaborative representation classification algorithm（CRC）,and synchronous orthogonal matching pursuit algorithm（SOMP）as comparisons.According to the experimental results,the overall classification accuracy of this paper’s algorithm on the Indian Pines dataset was 93.24%,and on the Pavia University Scene dataset was99.02%,and it reduced 0.27%and increased 1.62%respectively compared to SOMP algorithm which also combines spectral and spatial features.