Multispectral and hyperspectral image fusion has emerged as a highly effective technique for obtaining images with both high spatial and spectral resolution. This is an ill-posed problem that poses significant challenges to the optimization solution, which is often mitigated by incorporating low-rank and smooth priors to restrict the solution space. Traditionally, these priors are combined additively using nuclear norm and total variation (TV) regularization. However, the intricate interactions between these priors make it difficult to accurately characterize the prior structure using an additive approach. Moreover, their influence is heavily dependent on the trade-off parameter between the regularization terms. To address this issue, we propose a novel fusion method leveraging a joint low-rank and smooth tensor prior (LRST). The LRST method introduces a tensor nuclear norm on the gradient maps of various dimensions of the target image capitalizing on the analogous manifold structures shared between the original image and its gradient map, which seamlessly integrates the two priors into a unified regularization framework. This facilitates the precise and convenient exploitation of spatial and spectral correlations inherent in the desired hyperspectral image. Experimental findings demonstrate that compared to state-of-the-art fusion methods, the LRST approach yields finely fused images.

In the field of hyperspectral unmixing, deep learning has received increasing attention due to its powerful learning and data representation capabilities. Autoencoder is a popular technique for unmixing. Recently, an autoencoder-based depth image prior algorithm has been proposed for hyperspectral unmixing, which employs geometric methods to extract endmembers. The performance of this network solely focuses on estimating the abundance of images, and it has achieved good unmixing results. However, the depth image only employs one core network, which makes it highly vulnerable to noise and can lead to unstable unmixing outcomes. To address the aforementioned issue, this paper proposes a collaborative consistency autoencoder-based hyperspectral unmixing approach with deep image prior (CCAUDIP). For the proposed CCAUDIP model, it adopts two autoencoders to cooperatively handle the same input data to enhance the generalization ability of the network. Additionally, a consistency constraint is introduced to restrict the abundance outputs of the two core autoencoders and improve the robustness of the network. The experimental results show that the CCAUDIP method can achieve better unmixing results compared to other advanced unmixing algorithms.

Spectral unmixing is a crucial aspect of hyperspectral image processing. Given the low spatial resolution of hyperspectral remote sensing sensors, combined with the complexity and diversity of actual ground objects, hyperspectral remote sensing images often contain numerous mixed pixels, which make spectral unmixing a challenging task. Recent advancements in spectral libraries have shown promising results for decomposing mixed pixels in hyperspectral remote sensing images. Sparse unmixing, a semi-supervised unmixing strategy, avoids the drawbacks of blind source unmixing algorithms, which may extract virtual endmembers with no physical meaning. In this paper, we propose the multiscale spatial sparse unmixing (MSSU) algorithm, which utilizes the signal adaptive spatial multiscale unmixing of the over-segmentation method to decompose the complex unmixing problem. Furthermore, weighting factors are introduced to extract spatial information from the spectral image. The experimental results obtained from simulated hyperspectral datasets reveal the great potential of the proposed algorithm in unmixing.

As the spectral library continues to expand, sparse hyperspectral unmixing methods have been developed to solve the mixing problem without the need for end-member extraction or generation. These methods leverage the intrinsic spectral and spatial information to enhance the accuracy of fractional abundance estimation. However, their effectiveness is limited by rigid spatial regularization and insufficient utilization of spectral spatial information, which hampers the improvement of unmixing performance. To overcome this limitation, we present a novel algorithm named Local Spectral Similarity Guided Sparse Hyperspectral Unmixing with Spatial Graph Regularization (SGSU). In SGSU, we introduce a spatial graph regularization to enforce the inter-pixel correlation within spatial clusters and assign them to corresponding abundance vectors. To reduce the computational cost, we employ an adaptive superpixel-based spatial grouping strategy to segment the hyperspectral image, which translates the intrinsic geometry into constraints on abundance. Furthermore, we introduce a weighting factor with two components into the sparse unmixing framework. One component is based on the row sparsity of the estimated abundances, indicating the presence of active end-members; the other component is based on the similarity between neighboring pixels, which promotes piecewise smoothness of the estimated abundances. To obtain a more robust solution, we adopt a double-loop scheme based on the alternating direction method of multipliers (ADMM) algorithm to solve the SGSU model. Experimental results on both simulated and real hyperspectral datasets demonstrate that the proposed SGSU algorithm outperforms state-of-the-art sparse unmixing methods in terms of both accuracy of abundance estimation and end-member identification from spectral libraries. Our algorithm achieves superior unmixing results, which indicates its potential for practical applications in hyperspectral imaging.

Sparse unmixing is a semi-supervised method whose pur-pose is to find the best subset of library entries from the spec-tral library that best model the image. In sparse unmixing, the current main development direction is to incorporate the spatial information of the image into the model. Existing spa-tial sparse unmixing algorithms mainly use spatial weights or spatial regularization to characterize the spatial correlation between pixels to improve the unmixing results. For the complex and diverse hyperspectral data in reality, most al-gorithms are only good at processing a single scene, which brings greater challenges to their practicality. In order to ad-dress this issue, a new dual spatial weighted sparse unmixing model (DSWSU) is proposed, which simultaneously ex-ploits the spatially homogeneous information of images. For the proposed DSWSU, a pre-calculated superpixel weighting factor is designed to mitigate the effect of noise on unmixing. Meanwhile, the spatial neighborhood weighting factor aims to promote the local smoothness of the abundance maps. As a simple unmixing model, the proposed DSWSU can be quickly solved by the alternating direction multiplier method (ADMM). Experimental results on simulated hyperspectral data indicate that the proposed DSWSU method can achieve accurate abundance estimation in various scenarios (low or high noise interference), and obtain better unmixing results than other state-of-the-art unmixing algorithms.

Spectral unmixing is an essential technology for the interpretation of hyperspectral remote sensing images. Sparse unmixing has become a research hotspot in the field of spectral unmixing since it circumvents the issue of endmember extraction. Regularization based on spatial information further improves the performance of sparse unmixing. However, multiple regularization terms increase the complexity of the sparse model and the difficulty of regularization parameter tuning. To overcome this drawback, a new dual reweighted low-rank and total variation sparse unmixing (DRLRSU-TV) method is proposed, which jointly imposes the low-rank constraint, dual reweighted sparse constraint and total variation (TV) regularizer on the classic sparse unmixing model via two regularization terms. Experiment results on simulated hyper-spectral data verify the excellent unmixing performance of the proposed algorithm compared to other state-of-the-art sparse unmixing methods.

In the field of hyperspectral unmixing (HU), deep learning (DL) techniques have attracted increasing attention due to their powerful capabilities in learning and feature extraction. The autoencoder framework has flexible scalability as well as good unsupervised learning ability, and it achieves good performance in hyperspectral unmixing. However, some traditional autoencoder-based algorithms only focus on pixel-level reconstruction loss, which ignores the detailed information contained in the material. In addition, these algorithms usually only use a single autoencoder with non-convex properties, which brings great difficulty to the solution. In this paper, a cascaded autoencoders-based spectral-spatial unmixing (CASSU) framework is proposed to address these issues. For the proposed CASSU, on the one hand, two concatenated autoencoders are introduced to better find the global optimal solution. On the other hand, in this cascaded deep network, spectral angle mapping (SAM) and convolution operations are used to extract the spectral-spatial information of the image. Experimental results on real hyperspectral data indicate that the newly proposed CASSU algorithm has better unmixing performance compared to several state-of-the-art unmixing algorithms.

Hyperspectral unmixing is an important image interpre-tation technique that aims to estimate the pure constituent materials (endmembers) and their corresponding fractional abundances in each mixed pixel. Nonnegative matrix factorization (NMF) has attracted a lot of attention because of its ability to solve mixed pixel scenarios. The sparse NMF method achieves better unmixing results thanks to its full use of the sparse characteristics of the data. However, most existing sparse NMF unmixing techniques lack the consid-eration of spatial information. In fact, hyperspectral images contain intrinsic geometric information as well as rich spatial information. In this paper, a spatial graph regularized nonneg-ative matrix factorization unmixing framework (SGNMF) is established. For the proposed SGNMF, on the one hand, the graph regularization is introduced to characterize the latent manifold structure of the data, and on the other hand, the spatial weighting factor is used to mine the spatial correlation between pixels. The optimization problem of the SGNMF model can be solved by a multiplicative iterative rule. Exper-imental results on synthetic data sets indicate that the newly proposed SGNMF method is able to produce better results than other advanced spectral unmixing algorithms.

Remotely sensed hyperspectral images contain several bands (at about adjoining frequencies) for a similar zone on the surface of the Earth. Hyperspectral unmixing is a significant method for breaking down hyperspectral images into the components (endmembers) that conform each (potentially mixed) pixel and their abundance maps. Nonnegative matrix factorization (NMF) has attracted huge consideration because of the way that it can address mixed pixel scenarios. Most existing NMF unmixing techniques do not include spatial information in the analysis. An ongoing trend is to fuse the spatial and the spectral information contained in hyperspectral scenes to improve the solution. In this article, we build up another hyperspectral unmixing technique named spectral–spatial weighted sparse NMF (SSWNMF), in which two weighting factors are acquainted into the NMF model to upgrade the sparsity of the solution and capture the piecewise smooth structure of the data. We adopt a multiplicative iterative strategy to implement the proposed SSWNMF model. Our experimental results, conducted with both synthetic and real hyperspectral data, uncover that the proposed SSWNMF strategy can get accurate unmixing results over those gave by other unmixing strategies, with less parameter tuning.

With the increase of available spectral libraries, sparse unmixing has attracted great attention in the field of hyperspectral image unmixing. When the spatial information is integrated into the traditional sparse unmixing model, it achieves better performance. However, the less accurate description of the spatial structure limits the performance of the previous spatial sparse unmixing methods. To address this limitation, a new technique called superpixel based low-rank sparse unmixing (SpLRSU) is established, which encourages the local spatial consistency and the spatial continuity of the image. Specifically, superpixel segmentation is used to adaptively generate local homogeneous regions, and then the low-rank constraint is enforced on the abundance vectors of each spatial group to preserve the low-dimensional structure of superpixel blocks. Meanwhile, the spectral-spatial weighted sparse regularization term is introduced to promote the sparsity of fractional abundances in the spectral and spatial domains. The experimental results on the synthetic data set show that the newly proposed algorithm is superior to other advanced sparse unmixing algorithms.

Spectral unmixing is an important technique for hyperspectral image application, which aims to estimate the pure spectral signatures in each mixed pixel and their corresponding fractional abundances. However, due to the influence of factors such as illumination, topography change and atmosphere, spectral variability is inevitable, which will lead to inaccurate unmixing results. Traditional unmixing methods fail to handle this problem, especially the complex spectral variability in the image. To address this limitation, a new technique called low-rank subspace unmixing (LRSU) was established, which aims to jointly estimate a subspace projection and abundance maps. For the proposed LRSU approach, the original data is projected into a low-rank subspace to deal with various spectral variabilities in spectral unmixing. Meanwhile, the spectral-spatial weighted sparse regularization term is introduced to upgrade the sparsity of the solution and capture the piecewise smooth structure of the data. The experimental results, conducted using synthetic data sets, quantitatively indicate that the proposed LRSU strategy produces better results than other advanced spectral unmixing methods.

Hyperspectral unmixing is a technique for selecting endmembers (pure spectral constituents) and their abundances (proportions). Recently, sparse unmixing is a semi-supervised method in which mixed pixels are represented in the form of combinations of a number of pure spectral signatures from a large spectral library. Compared with other methods, the sparse unmixing method exhibits significant advantages. However, most of these sparse unmixing methods were implemented in spatial domain, where the information is too scattered, redundant and susceptible to noise. In this paper, we propose a new unmixing method called spectral-spatial weighted sparse unmixing in the transform domain (SSTSU) to impose the abundance sparsity and enhance the anti-noise performance. The experimental results show that the proposed algorithm has better anti-noise performance and unmixing results compared with other advanced sparse unmixing methods.

Hyperspectral unmixing aims to decompose a hyperspectral image (HSI) into a collection of constituent materials, or end-members, and their corresponding abundance fractions. Recently, nonnegative tensor factorization (NTF)-based spectral unmixing methods have attracted significant attention owing to their outstanding performance when representing an HSI without any information loss. However, tensor factorization-based HSI methods do not fully exploit the spatial contextual information present in the scene. Besides, these approaches are sensitive to low signal-to-noise ratio (SNR) in HSIs. To address this limitation, we propose a new spectral-spatial weighted sparse nonnegative tensor factorization (SSWNTF) method to preserve the spatial details in the abundance maps via the spectral and spatial weighting factors. Our experiments with simulated data sets certified that the proposed method outperforms other advanced methods.

Sparse representation-based approaches have been successfully applied to remotely sensed hyperspectral image unmixing. In recent years, sparse unmixing techniques have incorporated spatial information into the sparse unmixing model, achieving improved fractional abundance results. Most spatial-based sparse unmixing methods utilize regular-shaped neighborhoods (e.g., a cross or a square window) to characterize the spatial-contextual information around each pixel. However, the spatial characteristics of natural scenes are not always uniform, but vary according to the observed objects. Therefore, assuming uniform spatial neighborhoods may not be consistent with real spatial structures in the scene. Super-pixels offer a good solution to this problem since they can better characterize such spatial structures. Based on this observation, in this paper we develop a new superpixel-guided sparse unmixing (SPGSU) method for hyperspectral scenes. The proposed SPGSU includes the spatial correlation through a superpixel-based technique rather than assuming predefined pixel grids. Each superpixel can be regarded as a small spatial region, whose shape and size can be adaptively changed to accommodate different spatial structures. Our experimental results, conducted using simulated data sets, quantitatively indicate that our newly proposed method produces better results than other advanced spectral unmixing methods.

Spectral unmixing aims at estimating the fractional abundances of a set of pure spectral materials (endmembers) in each pixel of a hyperspectral image. The wide availability of large spectral libraries has fostered the role of sparse regression techniques in the task of characterizing mixed pixels in remotely sensed hyperspectral images. A general solution for sparse unmixing methods consists of using the l2regularizer to control the sparsity, resulting in a very promising performance but also suffering from sensitivity to large and small sparse coefficients. A recent trend to address this issue is to introduce weighting factors to penalize the nonzero coefficients in the unmixing solution. While most methods for this purpose focus on analyzing the hyperspectral data by considering the pixels as independent entities, it is known that there exists a strong spatial correlation among features in hyperspectral images. This information can be naturally exploited in order to improve the representation of pixels in the scene. In order to take advantage of the spatial information for hyperspectral unmixing, in this paper, we develop a new spectral-spatial weighted sparse unmixing (S2WSU) framework, which uses both spectral and spatial weighting factors, further imposing sparsity on the solution. Our experimental results, conducted using both simulated and real hyperspectral data sets, illustrate the good potential of the proposed S2WSU, which can greatly improve the abundance estimation results when compared with other advanced spectral unmixing methods.

Spectral unmixing is an important technique for hyperspectral data exploitation. In order to solve the unmixing problem using a collection of previously available spectral signatures (i.e., a spectral library), sparse unmixing aims at finding the optimal subset of endmembers to represent the pixels in a hyperspectral image. The classic collaborative unmixing globally assumes that all pixels in a hyperspectral scene share the same active set of endmembers. This assumption rarely holds in practice, as endmembers tend to appear localized in spatially homogeneous areas rather than spread over the whole image. To address this limitation, in this letter, we introduce a new strategy to preserve local collaborativity for sparse hyperspectral unmixing. The proposed approach, which is called local collaborative sparse unmixing, considers the fact that endmember signatures generally appear distributed in local spatial regions instead of uniformly distributed throughout the scene. The proposed approach, which includes spatial information in the standard collaborative formulation, has been experimentally validated using both simulated and real hyperspectral data sets.

Nonnegative matrix factorization (NMF), which can lead to nonsubtractive parts-based representation, has been demonstrated to be effective for dimensionality reduction of hyperspectral imagery (HSI). However, existing NMF methods applied to HSI use only a single spectral feature and do not take into consideration spatial information, such as texture or morphological features, while it has been widely acknowledged that exploiting multiple features can improve performance. Consequently, a variant of orthogonal NMF, which can not only achieve a nonnegative factorization but also exploit the complementary information that arises among heterogeneous features, is proposed for hyperspectral dimensionality reduction. The proposed method, which couples orthogonal NMF with a previous multiple-features-combining algorithm, yields a discriminative low-dimensional feature representation that matches the intuition that parts should sum to produce a whole. An efficient multiplicative updating procedure is derived, and its local convergence is guaranteed theoretically. Experimental results on two hyperspectral data sets demonstrate the effectiveness of the proposed method.

This paper address issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the curvelet domain. First, we observe that statistical distribution with heavy algebraic tails, such as the alpha-stable family, are in many cases more accurate modeling tools for the curvelet coefficients than families with exponential tails such as generalized Gaussian. Motivated by our modeling results, we then design a new processor for blind watermark detection using the Cauchy member of the alpha-stable family. We analyze the performance of the new detector in terms of the associated probabilities of detection and false alarm and we compare it to the performance of the generalized Gaussian detector and the traditional correlation-based detector by performance experiments. The experiments prove that Cauchy detector is superior to the others.

One of the problems encountered in image transmission is the cut-off or error of a bits chain at the moment of transmission. To protect the transmitted signal, it is necessary to couple quantized transform coding with a redundant transform. Ridgelet transform is a new directional resolution transform and it is more suitable for describing the signals with line or super-plane singularities. Finite ridgelet transform is a discrete orthonormal version of ridgelet transform proposed by Minh N.Do and Martin Vetterli. In this paper, we propose a new conception of redundant ridgelet transform, which we implement it mainly by controlling the ratio of the redundancy at the step of Radon transform in the ridgelet transform. We first briefly introduce the concept of ridgelet transform. Then, we illustrate finite ridgelet transform and the new method. Finally, the main features of the redundant ridgelet transform and its applications for image coding and image analysis are discussed.