• Deep Unsupervised Convolutional Kernels: A deep hierarchical NMF architecture is proposed to learn multi-layer convolution kernels in an unsupervised manner. • Unsupervised Hybrid Spectral-Spatial Modules: Novel synergistic integration of PCA, Whitening, NMF, Convolution, ReLU, and texture-aware LBP features. • Progressive Feature Abstraction: Multi-layer NMF framework enables progressively abstract, discriminative feature learning from unlabeled HSI data. • Breaks Shallow NMF Barrier: First deep NMF extension overcoming traditional limitations, capturing complex HSI structures efficiently. • Maintains Efficiency & Interpretability: Combines CNN-like hierarchical feature learning with NMF’s computational efficiency and inherent interpretability. Hyperspectral image (HSI) classification is a key task in remote sensing but significantly limited by the scarcity of labeled training samples. Traditional Nonnegative Matrix Factorization (NMF) provides interpretable representation but lacks the depth to extract discriminative features for complex HSI data. Deep learning methods, while powerful, require abundant labels that are often unavailable. To address this, we propose DNMFNet that a deep NMF network for unsupervised feature extraction. Its core innovation lies in learning hierarchical convolutional kernels via NMF without supervision, enabling deep representation learning under extreme label scarcity. Specifically, we extend NMF into a multi-layer architecture that integrates PCA, whitening, NMF convolution, and ReLU operations, forming modules capable of extracting rich spectral-spatial features. A classification framework built on these features is then developed. Experiments on three benchmark HSI datasets demonstrate that DNMFNet consistently outperforms state-of-the-art methods designed for few-shot learning.

Convolutional neural networks (CNNs) have shown impressive performance in hyperspectral image (HSI) classification. However, these deep learning methods still face two major challenges. One is that they require a large number of training samples to train parameters, and the other is that high-dimensional nonlinear feature extraction and multi-source information fusion. This paper proposes a deep stochastic adaptive Fourier decomposition (SAFD) network integrated with back-propagation (BP) and multi-scale feature fusion to significantly improve classification accuracy. The main contributions are threefold: 1) A deep SAFD network with BP is designed, which introduces BP into the deep SAFD network for the first time, and achieves automatic dynamic optimization of network parameters through the back-propagation algorithm. 2) A Kalman filter-based multi-scale pyramid construction method is proposed, which extracts hierarchical spatial features through state recursion equations and enhances texture representation by fusing local binary patterns (LBP). 3) An efficient classification algorithm based on a deep stochastic adaptive Fourier decomposition network with a BP algorithm is developed to integrate deep SAFD features, multi-scale pyramid features, and LBP texture features, achieving higher classification accuracy. Experimental results show that the proposed method outperforms other selected HSI classification methods with similar principles. Moreover, compared with other state-of-the-art deep learning methods, the proposed method can achieve better classification performance.

Deep learning-based hyperspectral image (HSI) classification methods have recently shown excellent performance. However, the success of these deep learning methods mainly relies on the deep network architecture with a huge amount of parameters trained by a large number of training samples. In this article, a deep high-order tensor sparse representation (SR) network (DHTSRNet) is proposed, which can obtain better classification results in the case of small training samples. Specifically, we propose a high-order tensor SR (HTSR) model that can handle arbitrary-order tensor-type data, and extend it to a deep HTSR model that can be used to train deep high-order tensor filters and features. Then, a deep feature extraction network (DHTSRNet) based on the deep HTSR model is constructed, which is used for feature extraction of HSI. Finally, an HSI classification method is constructed by combining DHTSRNet and the classifier based on graph-based learning (GSL), which can obtain better classification results in the case of small training samples. Experimental results show that the DHTSRNet can obtain better classification performance compared with other state-of-the-art HSI classification methods.

Deep learning-based hyperspectral image (HSI) classification methods have recently shown excellent performance, however, there are two shortcomings that need to be addressed. One is that deep network training requires a large number of labeled images, and the other is that deep network needs to learn a large number of parameters. They are also general problems of deep networks, especially in applications that require professional techniques to acquire and label images, such as HSI and medical images. In this paper, we propose a deep network architecture (SAFDNet) based on the stochastic adaptive Fourier decomposition (SAFD) theory. SAFD has powerful unsupervised feature extraction capabilities, so the entire deep network only requires a small number of annotated images to train the classifier. In addition, we use fewer convolution kernels in the entire deep network, which greatly reduces the number of deep network parameters. SAFD is a newly developed signal processing tool with solid mathematical foundation, which is used to construct the unsupervised deep feature extraction mechanism of SAFDNet. Experimental results on three popular HSI classification datasets show that our proposed SAFDNet outperforms other compared state-of-the-art deep learning methods in HSI classification.

The convolutional sparse coding (CSC) can learn shift-invariant convolution kernels. In deep convolutional neural networks, it takes a lot of time to train the convolution kernels. In this letter, a deep two-stage CSC network (DTCSCNet) is proposed, which can be used to simultaneously extract spatial features and spectral features from hyperspectral image (HSI) without back propagation and fine-tuning process, thus saving a lot of time. Furthermore, to further improve the performance of the network, we incorporate multiscale information. After deep feature extraction using DTCSCNet, we further investigate the classification performance of different classifiers on the extracted features. Experimental results show that the proposed method can obtain better classification performance compared with some closely related HSI classification methods.

Recently, hyperspectral image (HSI) classification methods based on deep learning have demonstrated excellent performance. However, these deep learning methods still face two major challenges. One is that they require a large number of labeled samples, and the other is that training parameters takes a lot of time. In this paper, we propose a dual-branch deep stochastic adaptive Fourier decomposition (SAFD) network (DSAFDNet) to alleviate the aforementioned two issues in HSI classification applications. SAFD is a newly developed signal processing tool with solid mathematical foundation. It can be used to find common filters (i.e. convolution kernels) of a set of random signals or multi-signals. Since the convolution kernels obtained by SAFD decomposition are complex numbers, few deep learning methods directly deal with such complex convolution kernels. To this end, we propose a dual-branch network to extract deep features from hyperspectral images using both real and imaginary parts of convolutional kernels. After deep feature extraction using DSAFDNet, we further investigate the classification performance of different classifiers on the extracted features. Experimental results show that the proposed method outperforms some HSI classification methods with similar principles. Moreover, compared with other state-of-the-art deep learning methods, the proposed method can achieve better classification performance.

Most hyperspectral image (HSI) data exist in the form of tensor; the tensor representation preserves the potential spatial–spectral structure information compared with the vector representation, which can help improve the classification performance of HSI. In this article, a deep high-order tensor convolutional sparse coding (CSC) model is proposed, which can be used to train deep high-order filters. Based on the deep high-order tensor CSC model, a deep feature extraction network (DHTCSCNet) is constructed, which is used for feature extraction of HSIs. By combining the spectral–spatial feature and the features extracted by the proposed DHTCSCNet at each layer, a combined feature that incorporates shallow, deep, spectral, and spatial features can be obtained. Then, the graph-based learning (GSL) methods are used to classify the combined feature. Experimental results show that the DHTCSCNet can obtain better classification performance compared with other HSI classification methods.

Deconvolutional networks have attracted extensive attention and have been successfully applied in the field of computer vision. In this paper we propose a novel two-branch deconvolutional network (TBDN) that can improve the performance of conventional deconvolutional networks and reduce the computational complexity. A feasible iterative algorithm is designed to solve the optimization problem for the TBDN model, and a theoretical analysis of the convergence and computational complexity for the algorithm is also provided. The application of the TBDN in stereo matching is presented by constructing a disparity estimation network. Extensive experimental results on four commonly used datasets demonstrate the efficiency and effectiveness of the proposed TBDN.