Hyperspectral Unmixing Using Double Reweighted Sparse Regression and Total Variation

Sparse unmixing has become a popular tool for hyperspectral imagery interpretation. It refers to finding the optimal subset of a spectral library to reconstruct the image data and further estimate the proportions of different materials. Recently, multi-objective based sparse unmixing methods have presented promising performance because of their advantages in addressing combinatorial problems. A spectral and multi-objective based sparse unmixing (SMoSU) algorithm was proposed in our previous work, which solves the decision-making problem well. However, it does not show outstanding advantages in strong noise cases. To solve the problem, in this paper, SMoSU is improved based on the estimation of distribution algorithms (EDAs). The machine learning based EDAs have been a reliable approach in solving multi-objective problems. However, most of them are for special problems and relatively weak in theoretical foundations. Thus, it is unreliable to extend it directly to sparse unmixing. Here, we improve EDA on the basis of classification and propose a classification-based model for individual generating under the framework of SMoSU (CM-MoSU). In CM-MoSU, the whole population is divided to be positive and negative. Then, the macroinformation of positive individuals is used to guide the generation of new individuals. Therefore, the optimization task could pay more attention to the feasible space with high quality. Moreover, some theoretical analyses are presented to prove the reliability of CM-MoSU. In experiments, several state-of-the-art sparse unmixing algorithms are compared. Both synthetic and real-world experiments demonstrate the effectiveness of CM-MoSU.

Spectral unmixing aims at identifying the pure spectral signatures in hyperspectral images and simultaneously estimating their proportions in each pixel of the scene. By using an available spectral library as a dictionary, sparse-regression-based approaches aim at finding a subset of the dictionary that can optimally model each pixel in a given hyperspectral image. regularizer has been widely considered as a regularization strategy to exploit the sparsity of the unmixing solution. Further sparsity can be imposed by also using weighting factors. However, most existing strategies focus on the unmixing solution ignoring the gradient information. To account for the gradient information in hyperspectral unmixing, we propose a weighted sparse regression with total variation (WSRTV) unmixing model. The proposed WSRTV model incorporates gradient information in the sparse regression formulation by means of the weighted total variation (WTV) regularizer. The model imposes sparsity on both the solution and the gradient to improve the performance of unmixing. A dual symmetric Gauss-Seidel alternating direction method of multipliers (sGSADMM) is designed to optimize the proposed model. The designed algorithm both handles the anisotropic and isotropic WTV. Simulated and real hyperspectral data demonstrate the effectiveness of the proposed framework.

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.

Recently, the multiobjective evolutionary algorithms (MOEAs) have been designed to cope with the sparse unmixing problem. Due to the excellent performance of MOEAs in solving the NP hard optimization problems, they have also achieved good results for the sparse unmixing problems. However, most of these MOEA-based methods only deal with a single pixel for unmixing and are subjected to low efficiency and are time-consuming. In fact, sparse unmixing can naturally be seen as a multitasking problem when the hyperspectral imagery is clustered into several homogeneous regions, so that evolutionary multitasking can be employed to take advantage of the implicit parallelism from different regions. In this paper, a novel evolutionary multitasking multipopulation particle swarm optimization framework is proposed to solve the hyperspectral sparse unmixing problem. First, we resort to evolutionary multitasking optimization to cluster the hyperspectral image into multiple homogeneous regions, and directly process the entire spectral matrix in multiple regions to avoid dimensional disasters. In addition, we design a novel multipopulation particle swarm optimization method for major evolutionary exploration. Furthermore, an intra-task and inter-task transfer and a local exploration strategy are designed for balancing the exchange of useful information in the multitasking evolutionary process. Experimental results on two benchmark hyperspectral datasets demonstrate the effectiveness of the proposed method compared with the state-of-the-art sparse unmixing algorithms.

Sparse unmixing has attracted much attention in recent years. It aims at estimating the fractional abundances of pure spectral signatures in mixed pixels in hyperspectral images. To exploit spatial-contextual information present in the scene, the total variation (TV) regularization is incorporated into the sparse unmixing formulation, promoting adjacent pixels having similar not only endmembers but also fractional abundances, and thus having similar structural sparsity. It is therefore hoped to impose joint sparsity, instead of classic single sparsity, on these adjacent pixels to further improve the unmixing performance. To this end, we include the joint-sparse-blocks regression into the TV spatial regularization framework and present a new unmixing algorithm, termed joint-sparse-blocks unmixing via variable splitting augmented Lagrangian and total variation (JSBUnSAL-TV). In particular, a reweighting strategy is utilized to enhance sparsity along lines within each block. Simulated and real-data experiments show the advantages of the proposed algorithm.

Multi-objective based spectral unmixing for hyperspectral images

The acquired hyperspectral data are always in low resolution in both spatial and spectral domains, which will result in lots of mixed pixels and degrade the detection and recognition performance in civil and military applications. So many super resolution techniques are applied to overcome this limit. In this paper, we propose a coupled hyperspectral spatial super-resolution and spectral unmixing method based on sparse representation. Combing spatial super-resolution and spectral unmixing can precisely conserve both spatial information and spectral correlation among different bands. Spectral unmixing is taken as a regularization term in spatial super-resolution to test spectral consistency and avoid spectral distortion, while spatial super-resolution is used to enhance the resolution of abundance map after spectral unmixing.

Hyperspectral unmixing (HSU), which aims to identify constituent materials and estimate the corresponding proportions in a scene, is an essential research topic in remote sensing. Most deep learning-based methods are data-inspired, relying on massive amounts of data to train black-box-like networks. While a few model-inspired unmixing networks only consider the spectral features of the pixel, ignoring the exploration of spatial information between pixels. In this paper, we design a network topology according to the classical iterative algorithm, and the large number of learnable parameters contained in the network are continuously updated through data fitting. In other words, we integrate the concepts of both model-driven and data-driven and propose a deep interpretable fully convolutional neural network (DIFCNN). The iteration of the classic sparse unmixing algorithm is unfolded to provide guidance for the network structure and incorporate prior knowledge into the network. Meanwhile, two-dimensional (2D) convolutional layers are employed to automatically learn the spatial information at different scales. A known spectral library is used as a prior to initialize network parameters and reconstruct the image. The DIFCNN adopts an end-to-end training strategy, in addition, we establish a new loss function that adds a joint sparse constraint on the abundance result to the cross-entropy loss. Experiments on both synthetic and real datasets show that the performance of the DIFCNN not only outperforms the SUnSAL and its improved algorithms, but also is highly competitive in the state-of-the-art methods of deep learning.

Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details. A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework. The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively. In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

The preservation of discontinuous edges in seismic dataset such as faults, fractures, pinch-outs, channels and salt bodies while attenuating random noise is of great significance for the following seismic data interpretation. Noise reduction using inversion with total variation (TV) regularization is a kind of 2D edge-preserving filtering method. However, TV regularization is only limited to 2D data. In this paper, we extend the 2D method to 3D case by firstly taking difference of seismic data along different directions, and then performing Cauchy regularization. A synthetic 3D dataset, a real stacked OBC dataset and a real stacked land dataset are used to illustrate the performance of the method. The results show that the 3D seismic noise-reduction method we proposed can perfectly preserve edges of 3D discontinuous events while reducing random noise. In addition, there is no obvious trail of noise along the spatial directions since 3D noise-reduction scheme is adopted.

Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging process. In the past decades, total variation regularization played a dominant role in the literature. Two forms of total variation regularizations, namely the first-order and the second-order total variation (TV-1 and TV-2) have been widely used. TV-1 has a disadvantage: it reconstructs images in the form of piece-wise constants when the noise and/or under-sampling is severe, while TV-2 reconstructs natural-looking images under such scenarios. On the other hand, TV-1 can recover sharp jumps better than TV-2. Two forms of generalizations, namely Hessian-Schatten norm (HSN) regularization, and total generalized variation (TGV) regularization, have been proposed and have become significant developments in the area of regularization for imaging inverse problems owing to their performance. While the strength of TGV is that it can combine the advantages of TV-1 and TV-2, HSN has better structure-preserving property. Here, we develop a novel regularization for image recovery that combines the strengths of TGV and HSN. We achieve this by restricting the maximization space in the dual form of HSN in the same way that TGV is obtained from TV-2. We call the new regularization the generalized Hessian-Schatten norm regularization (GHSN). We develop a novel computational method for image reconstruction using the new form of regularization based on the well-known framework called the alternating direction method of multipliers (ADMM). We demonstrate the strength of the GHSN using some reconstruction examples.

Hyperspectral unmixing is a technique that can be used to find the materials and their corresponding proportions present in observed mixed pixels. It has been widely used for hyperspectral data exploitation. Traditionally, this problem is solved using the constrained least squares optimization, which would lead to a dense solution. In recent years, researchers have observed that the number of materials in a mixed pixel is generally much smaller than the whole number of materials present in a given scene. They proposed to solve the problem through sparse unmixing approaches, which generally lead to constrained optimization. These sparse unmixing approaches have received considerable attention over the past few years. From the perspective of Bayesian inference, these methods assume fixed priors. In this article, we propose to solve the spectral unmixing problem by using sparse Bayesian learning (SBL) framework. In contrast to the approaches that use fixed priors, SBL incorporates a hierarchical parameterized prior that encourages sparsity in representation in its Bayesian inference to obtain a sparse solution. Experimental results on simulated data sets and a real hyperspectral scene demonstrate that the proposed method can achieve good performance compared with some state-of-the-art sparse unmixing algorithms. Our results also show that the proposed method can achieve good performance with a set of default parameter settings.

We introduce a total variation (TV) regularization model for synthetic aperture radar (SAR) image despeckling. A dual-formulation-based adaptive TV (ATV) regularization method is applied to solve the TV regularization. The parameter adaptation of the TV regularization is performed based on the noise level estimated via wavelets. The TV-regularization-based image restoration model has a good performance in preserving image sharpness and edges while removing noises, and it is therefore effective for edge preserve SAR image despeckling. Experiments have been carried out using optical images contaminated with artificial speckles first and then SAR images. A despeckling evaluation index (DEI) is designed to assess the effectiveness of edge preserve despeckling on SAR images, which is based on the ratio of the standard deviations of two neighborhood areas of different sizes of a pixel. Experimental results show that the proposed ATV method can effectively suppress SAR image speckles without compromising the edge sharpness of image features according to both subjective visual assessment of image quality and objective evaluation using DEI.

Reweighted sparse unmixing for hyperspectral images with noise level estimation

To solve the ill-posed problem in electrical impedance tomography (EIT) and overcome the blur effect made by conventional L2 Tikhonov regularization, a new two-step iterative regularization algorithm is applied for the process reconstruction of lung respiration. This algorithm is based on total variation (TV) regularization method, and uses a two-step iterative method with TV denoising operator, so that it can achieve double regularization effect. This algorithm has advantages in both resolution and robustness. Both simulation and experiment results are executed to prove the effectiveness of TV regularization method.