Deep subspace clustering methods are now prominent in clustering, typically using fully connected networks and a self-representation loss function. However, these methods often struggle with overfitting and lack interpretability. In this paper, we explore an alternative clustering approach based on deep unfolding. By unfolding iterative optimization methods into neural networks, this approach offers enhanced interpretability and reliability compared to data-driven deep learning methods, and greater adaptability and generalization than model-based approaches. Hence, unfolding has become widely used in inverse imaging problems, such as image restoration, reconstruction, and super-resolution, but has not been sufficiently explored yet in the context of clustering. In this work, we introduce an innovative clustering architecture for hyperspectral images (HSI) by unfolding an iterative solver based on the Alternating Direction Method of Multipliers (ADMM) for sparse subspace clustering. To our knowledge, this is the first attempt to apply unfolding ADMM for computing the self-representation matrix in subspace clustering. Moreover, our approach captures well the structural characteristics of HSI data by employing the K nearest neighbors algorithm as part of a structure preservation module. Experimental evaluation of three established HSI datasets shows clearly the potential of the unfolding approach in HSI clustering and even demonstrates superior performance compared to state-of-the-art techniques.
A TRPCA-Inspired Deep Unfolding Network for Hyperspectral Image Denoising via Thresholded t-SVD and Top-K Sparse Transformer
College of Computer Science and Engineering, Shandong University of Science and Technology（计算机科学与工程学院，山东科技大学）；Gosci Information Technology Co.,Ltd.（Gosci信息技术有限公司）
1 School of Mathematics；Statistics, Xi'an Jiaotong University 2 School of Mathematics；Information Science, Shaanxi Normal University 3 Shenyang Institute of Automation, Chinese Academy of Sciences
In this paper, we propose a novel approach to hyperspectral image super-resolution by modeling the global spatial-and-spectral correlation and local smoothness properties over hyperspectral images. Specifically, we utilize the tensor nuclear norm and tensor folded-concave penalty functions to describe the global spatial-and-spectral correlation hidden in hyperspectral images, and 3D total variation (TV) to characterize the local spatial-and-spectral smoothness across all hyperspectral bands. Then, we develop an efficient algorithm for solving the resulting optimization problem by combing the l…
Physics-Guided Deep Unfolding for Blind Cross-Sensor Spectral Super-Resolution via Learning the Spectral Transformation Function
Center for Geo-Spatial Information, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（地理信息中心，深圳先进技术研究院，中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；Shenzhen Engineering Laboratory of Ocean Environmental Big Data Analysis and Application（深圳海洋环境大数据分析与应用工程实验室）
Xi’an Jiaotong University（西安交通大学）；Harbin Institute of Technology（哈尔滨工业大学）
Hyperspectral imaging can help better understand the characteristics of different materials, compared with traditional image systems. However, only high-resolution multispectral (HrMS) and low-resolution hyperspectral (LrHS) images can generally be captured at video rate in practice. In this paper, we propose a model-based deep learning approach for merging an HrMS and LrHS images to generate a high-resolution hyperspectral (HrHS) image. In specific, we construct a novel MS/HS fusion model which takes the observation models of low-resolution images and the low-rankness knowledge along the spec…
Spectral imaging enables spatially-resolved identification of materials in remote sensing, biomedicine, and astronomy. However, acquisition times require balancing spectral and spatial resolution with signal-to-noise. Hyperspectral imaging provides superior material specificity, while multispectral images are faster to collect at greater fidelity. We propose an approach for fusing hyperspectral and multispectral images to provide high-quality hyperspectral output. The proposed optimization leverages the least absolute shrinkage and selection operator (LASSO) to perform variable selection and r…
Magellium；ITAV-USR3505, université de Toulouse（图卢兹大学ITAV-USR3505）；CNES（法国国家空间研究中心）
In this paper, we address the issue of hyperspectral pan-sharpening, which consists in fusing a (low spatial resolution) hyperspectral image HX and a (high spatial resolution) panchromatic image P to obtain a high spatial resolution hyperspectral image. The problem is addressed under a variational convex constrained formulation. The objective favors high resolution spectral bands with level lines parallel to those of the panchromatic image. This term is balanced with a total variation term as regularizer. Fit-to-P data and fit-to-HX data constraints are effectively considered as mathematical c…
Universidad Rey Juan Carlos（胡安·卡洛斯国王大学）；Universidad Industrial de Santander（桑坦德工业大学）
In remote sensing, hyperspectral (HS) and multispectral (MS) image fusion have emerged as a synthesis tool to improve the data set resolution. However, conventional image fusion methods typically degrade the performance of the land cover classification. In this paper, a feature fusion method from HS and MS images for pixel-based classification is proposed. More precisely, the proposed method first extracts spatial features from the MS image using morphological profiles. Then, the feature fusion model assumes that both the extracted morphological profiles and the HS image can be described as a …
With the development of deep learning technology, multi-spectral image super-resolution methods based on convolutional neural network have recently achieved great progress. However, the single hyperspectral image super-resolution remains a challenging problem due to the high-dimensional and complex spectral characteristics of hyperspectral data, which make it difficult to simultaneously capture spatial and spectral information. To deal with this issue, we propose a novel Feedback Refined Local-Global Network (FRLGN) for the super-resolution of hyperspectral image. To be specific, we develop a …
Low-rankness is important in the hyperspectral image (HSI) denoising tasks. The tensor nuclear norm (TNN), defined based on the tensor singular value decomposition, is a state-of-the-art method to describe the low-rankness of HSI. However, TNN ignores some physical meanings of HSI in tackling denoising tasks, leading to suboptimal denoising performance. In this paper, we propose the multi-modal and frequency-weighted tensor nuclear norm (MFWTNN) and the non-convex MFWTNN for HSI denoising tasks. Firstly, we investigate the physical meaning of frequency slices and reconsider their weights to im…
Harbin Institute of Technology（哈尔滨工业大学）；Peng Cheng Laboratory（鹏城实验室）；Wuhan University（武汉大学）
To solve the ill-posed problem of hyperspectral image super-resolution (HSISR), an usually method is to use the prior information of the hyperspectral images (HSIs) as a regularization term to constrain the objective function. Model-based methods using hand-crafted priors cannot fully characterize the properties of HSIs. Learning-based methods usually use a convolutional neural network (CNN) to learn the implicit priors of HSIs. However, the learning ability of CNN is limited, it only considers the spatial characteristics of the HSIs and ignores the spectral characteristics, and convolution is…
Institut Charles Delaunay (CNRS), Université de Technologie de Troyes（特鲁瓦技术大学，夏尔·德洛内研究所（法国国家科学研究中心））；School of Engineering and Physical Sciences, Heriot-Watt University（赫瑞瓦特大学，工程与物理科学学院）；LITIS lab, Université de Rouen（鲁昂大学，LITIS实验室）
In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while th…
RWTH Aachen University（亚琛工业大学）；National Technical University of Athens（雅典国立技术大学）；Athena Research Center（雅典娜研究中心）
In this paper, we propose a new deep unfolding neural network based on the ADMM algorithm for analysis Compressed Sensing. The proposed network jointly learns a redundant analysis operator for sparsification and reconstructs the signal of interest. We compare our proposed network with a state-of-the-art unfolded ISTA decoder, that also learns an orthogonal sparsifier. Moreover, we consider not only image, but also speech datasets as test examples. Computational experiments demonstrate that our proposed network outperforms the state-of-the-art deep unfolding network, consistently for both real-…
Huazhong University of Science & Technology（华中科技大学）；Wuhan Jingce Electronic Group（武汉精测电子集团）
We present a simple, efficient, and scalable unfolding network, SAUNet, to simplify the network design with an adaptive alternate optimization framework for hyperspectral image (HSI) reconstruction. SAUNet customizes a Residual Adaptive ADMM Framework (R2ADMM) to connect each stage of the network via a group of learnable parameters to promote the usage of mask prior, which greatly stabilizes training and solves the accuracy degradation issue. Additionally, we introduce a simple convolutional modulation block (CMB), which leads to efficient training, easy scale-up, and less computation. Couplin…
Hyperspectral images are crucial for many research works. Spectral super-resolution (SSR) is a method used to obtain high spatial resolution (HR) hyperspectral images from HR multispectral images. Traditional SSR methods include model-driven algorithms and deep learning. By unfolding a variational method, this paper proposes an optimization-driven convolutional neural network (CNN) with a deep spatial-spectral prior, resulting in physically interpretable networks. Unlike the fully data-driven CNN, auxiliary spectral response function (SRF) is utilized to guide CNNs to group the bands with spec…
Deep Equilibrium Convolutional Sparse Coding for Hyperspectral Image Denoising
School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；College of Computer Science, Zhejiang University（浙江大学计算机科学学院）
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico（高等技术学院）
The recently proposed plug-and-play (PnP) framework allows leveraging recent developments in image denoising to tackle other, more involved, imaging inverse problems. In a PnP method, a black-box denoiser is plugged into an iterative algorithm, taking the place of a formal denoising step that corresponds to the proximity operator of some convex regularizer. While this approach offers flexibility and excellent performance, convergence of the resulting algorithm may be hard to analyze, as most state-of-the-art denoisers lack an explicit underlying objective function. In this paper, we propose a …
This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect spectrally and spatially similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special atte…
A Dual Symmetric Gauss-Seidel Alternating Direction Method of Multipliers for Hyperspectral Sparse Unmixing
School of Information Science and technology, and the Provincial Key Lab of Information Coding and Trans- mission, Southwest Jiaotong University（信息科学与技术学院，信息编码与传输省重点实验室，西南交通大学）；School of Mathematics, Southwest Jiaotong University（数学学院，西南交通大学）；School of Computer and Computing Science, Zhejiang University City College（计算机与计算科学学院，浙江大学城市学院）
Ruhr University Bochum（波鸿鲁尔大学）；Technical University Berlin（柏林工业大学）；Technical University of Munich（慕尼黑工业大学）
We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose …
Peking University Shenzhen Graduate School（北京大学深圳研究生院）；Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；Peking University（北京大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Peng Cheng Laboratory（鹏城实验室）
Hyperspectral imaging is an essential imaging modality for a wide range of applications, especially in remote sensing, agriculture, and medicine. Inspired by existing hyperspectral cameras that are either slow, expensive, or bulky, reconstructing hyperspectral images (HSIs) from a low-budget snapshot measurement has drawn wide attention. By mapping a truncated numerical optimization algorithm into a network with a fixed number of phases, recent deep unfolding networks (DUNs) for spectral snapshot compressive sensing (SCI) have achieved remarkable success. However, DUNs are far from reaching th…
Low-Rank Representations Meets Deep Unfolding: A Generalized and Interpretable Network for Hyperspectral Anomaly Detection
Aerospace Information Research Institute, Chinese Academy of Sciences（中国科学院空天信息创新研究院）；School of Mathematics and Statistics, Southeast University（东南大学数学学院与统计学院）；College of Resources and Environment, University of Chinese Academy of Sciences（中国科学院大学资源与环境学院）；Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK（格勒诺布尔阿尔卑斯大学、法国国家信息与自动化研究所、法国国家科学研究中心、格勒诺布尔理工学院、约瑟夫·傅里叶大学联合实验室）
Sparse model is widely used in hyperspectral image classification.However, different of sparsity and regularization parameters has great influence on the classification results.In this paper, a novel adaptive sparse deep network based on deep architecture is proposed, which can construct the optimal sparse representation and regularization parameters by deep network.Firstly, a data flow graph is designed to represent each update iteration based on Alternating Direction Method of Multipliers (ADMM) algorithm.Forward network and Back-Propagation network are deduced.All parameters are updated by …
Joint Superpixel and Self-Representation Learning for Scalable Hyperspectral Image Clustering
Department of Telecommunications and Information Processing（电信与信息处理系）；Ghent University（根特大学）；Royal Institute for Cultural Heritage (KIK-IRPA)（皇家文化遗产研究院）；School of Computer Science（计算机科学学院）；China University of Geosciences（中国地质大学）
Inter and Intra Prior Learning-based Hyperspectral Image Reconstruction Using Snapshot SWIR Metasurface
School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）；College of Information and Control Engineering, Xi’an University of Architecture and Technology（西安建筑科技大学信息与控制工程学院）；Sejong University（世宗大学）
Tsinghua University（清华大学）；Shenzhen Institute of Future Media Technology（深圳未来媒体技术研究院）；Westlake University（西湖大学）；ETH Zürich（苏黎世联邦理工学院）；University of Würzburg（维尔茨堡大学）
In coded aperture snapshot spectral compressive imaging (CASSI) systems, hyperspectral image (HSI) reconstruction methods are employed to recover the spatial-spectral signal from a compressed measurement. Among these algorithms, deep unfolding methods demonstrate promising performance but suffer from two issues. Firstly, they do not estimate the degradation patterns and ill-posedness degree from the highly related CASSI to guide the iterative learning. Secondly, they are mainly CNN-based, showing limitations in capturing long-range dependencies. In this paper, we propose a principled Degradati…
Model-Guided Network with Cluster-Based Operators for Spatio-Spectral Super-Resolution
Institute of Applied Computing and Community Code (IAC3)（应用计算与社区代码研究所）；Dept. of Mathematics and Computer Science, Universitat de les Illes Balears（数学与计算机科学系，巴利阿里大学）
GIPSA-Lab（格勒诺布尔图像、信号、自动化与控制实验室）；Grenoble Institute of Technology（格勒诺布尔理工学院）；Faculty of Electrical and Computer Engineering, University of Iceland（冰岛大学电气与计算机工程学院）
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These complementary characteristics have stimulated active research in the inference of images with high spatial and spectral resolutions from HSI-MSI pairs. In this paper, we formulate this data fusion problem as the minimization of a convex objective function containing two data-fitting terms and an edge-preserving regularizer. The data-fitting terms are quadratic and…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time. This premise has recently guided the research to the innovative and meaningful idea of imposing multiple constraints on the parameters involved in the problem under study. For instance, when dealing with problems whose parameters form sparse and low-rank matrices, the adoption of suitably combined constraints imposing sparsity and low-rankness, is expected …
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；GIPSA-Lab, Université de Grenoble（格勒诺布尔大学GIPSA实验室）；Grenoble Institute of Technology（格勒诺布尔理工学院）；University of Iceland（冰岛大学）
Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadrati…
$\ell_1$DecNet+: A new architecture framework by $\ell_1$ decomposition and iteration unfolding for sparse feature segmentation
School of Mathematical Sciences, Nankai University, Tianjin, China（南开大学数学科学学院）；Department of Mathematics, City University of Hong Kong, China（香港城市大学数学系）；School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China（南京航空航天大学数学学院）；Norwegian Research Centre (NORCE), Bergen, Norway（挪威研究交流中心）
