A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS

Uncertainty Assessment of Spectral Mixture Analysis in Remote Sensing Imagery

Spectral mixture analysis (SMA), a scheme of sub-pixel-based classifications, is one of the widely used models to map fractional land use and land cover information in remote sensing imagery. It assumes that: 1) a mixed pixel is composed by several pure land cover classes (endmembers) linearly or nonlinearly, and 2) the spectral signature of each endmember is a constant within the entire spatial extent of analysis. SMA has been commonly applied to impervious surface area extraction, vegetation fraction estimation, and land use and land cover change (LULC) mapping. Limitations of SMA, however, still exist. First, the existence of between- and within-class variability prevents the selection of accurate endmembers, which results in poor accuracy of fractional land cover estimates. Weighted spectral mixture analysis (WSMA) and transformed spectral mixture analysis (TSMA) are alternate means to address the within- and between- class variability. These methods, however, have not been analyzed systematically and comprehensively. The effectiveness of each WSMA and TSMA scheme is still unknown, in particular within different urban areas. Second, multiple endmember SMA (MESMA) is a better alternative to address spectral mixture model uncertainties. It, nonetheless, is time consuming and inefficient. Further, incorrect endmember selections may still limit model performance as the best-fit endmember model might not be the optimal model due to the existence of spectral variability. Therefore, this study aims 1) to explore endmember uncertainties by examining WSMA and TSMA modeling comprehensively, and 2) to develop an improved MESMA model in order to address the uncertainties of spectral mixture models. Results of the WSMA examination illustrated that some weighting schemes did reduce endmember uncertainties since they could improve the fractional estimates significantly. The results also indicated that spectral class variance played a key role in addressing the endmember uncertainties, as the better performing weighting schemes were constructed with spectral class variance. In addition, the results of TSMA examination demonstrated that some TSMAs, such as normalized spectral mixture analysis (NSMA), could effectively solve the endmember uncertainties because of their stable performance in different study areas. Results of Class-based MEMSA (C-MESMA) indicated that it could address spectral mixture model uncertainties by reducing a lot of the calculation burden and effectively improving accuracy. Assessment demonstrated that C-MEMSA significantly improving accuracy. Major contributions of this study can be summarized as follow. First, the effectiveness of addressing endmember uncertainties have been fully discussed by examining: 1) the effectiveness of ten weighted spectral mixture models in urban environments; and 2) the effectiveness of 26 transformed spectral mixture models in three locations. Constructive guidance regarding handling endmember uncertainties using WSMA and TSMA have been provided. Second, the uncertainties of spectral mixture model were reduced by developing an improved MESMA model, named C-MESMA. C-MESMA could restrict the distribution of endmembers and reduce the calculation burden of traditional MESMA, increasing SMA accuracy significantly

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Image fusion for spatial enhancement of hyperspectral image via pixel group based non-local sparse representation

Restricted by technical and budget constraints, hyperspectral images (HSIs) are usually obtained with low spatial resolution. In order to improve the spatial resolution of a given hyperspectral image, a new spatial and spectral image fusion approach via pixel group based non-local sparse representation is proposed, which exploits the spectral sparsity and spectral non-local self-similarity of the hyperspectral image. The proposed approach fuses the hyperspectral image with a high-spatial-resolution multispectral image of the same scene to obtain a hyperspectral image with high spatial and spectral resolutions. The input hyperspectral image is used to train the spectral dictionary, while the sparse codes of the desired HSI are estimated by jointly encoding the similar pixels in each pixel group extracted from the high-spatial-resolution multispectral image. To improve the accuracy of the pixel group based non-local sparse representation, the similar pixels in a pixel group are selected by utilizing both the spectral and spatial information. The performance of the proposed approach is tested on two remote sensing image datasets. Experimental results suggest that the proposed method outperforms a number of sparse representation based fusion techniques, and can preserve the spectral information while recovering the spatial details under large magnification factors