A Viking Lander 1 image was modeled as mixtures of reflectance spectra of palagonite dust, gray andesitelike rock, and a coarse rocklike soil. The rocks are covered to varying degrees by dust but otherwise appear unweathered. Rocklike soil occurs as lag deposits in deflation zones around stones and on top of a drift and as a layer in a trench dug by the lander. This soil probably is derived from the rocks by wind abrasion and/or spallation. Dust is the major component of the soil and covers most of the surface. The dust is unrelated spectrally to the rock but is equivalent to the global-scale dust observed telescopically. A new method was developed to model a multispectral image as mixtures of end-member spectra and to compare image spectra directly with laboratory reference spectra. The method for the first time uses shade and secondary illumination effects as spectral end-members; thus the effects of topography and illumination on all scales can be isolated or removed. The image was calibrated absolutely from the laboratory spectra, in close agreement with direct calibrations. The method has broad applications to interpreting multispectral images, including satellite images.

Spectral mixture modeling - A new analysis of rock and soil types at the Viking Lander 1 site. [on Mars]

The spectral signatures of the materials contained in hyperspectral images, also called endmembers (EM), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an image. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout the whole unmixing process and compromises the quality of its results. Therefore, large efforts have been recently dedicated to mitigate the effects of spectral variability in SU. This resulted in the development of algorithms that incorporate different strategies to allow the EMs to vary within a hyperspectral image, using, for instance, sets of spectral signatures known a priori, Bayesian, parametric, or local EM models. Each of these approaches has different characteristics and underlying motivations. This paper presents a comprehensive literature review contextualizing both classic and recent approaches to solve this problem. We give a detailed evaluation of the sources of spectral variability and their effect in image spectra. Furthermore, we propose a new taxonomy that organizes existing works according to a practitioner's point of view, based on the necessary amount of supervision and on the computational cost they require. We also review methods used to construct spectral libraries (which are required by many SU techniques) based on the observed hyperspectral image, as well as algorithms for library augmentation and reduction. Finally, we conclude the paper with some discussions and an outline of possible future directions for the field.

Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review

Endmember (EM) spectral variability can greatly impact the performance of standard hyperspectral image analysis algorithms. Extended parametric models have been successfully applied to account for the EM spectral variability. However, these models still lack the compromise between flexibility and low-dimensional representation that is necessary to properly explore the fact that spectral variability is often confined to a low-dimensional manifold in real scenes. In this article we propose to learn a spectral variability model directly from the observed data, instead of imposing it a priori . This is achieved through a deep generative EM model, which is estimated using a variational autoencoder (VAE). The encoder and decoder that compose the generative model are trained using pure pixel information extracted directly from the observed image, what allows for an unsupervised formulation. The proposed EM model is applied to the solution of a spectral unmixing problem, which we cast as an alternating nonlinear least-squares problem that is solved iteratively with respect to the abundances and to the low-dimensional representations of the EMs in the latent space of the deep generative model. Simulations using both synthetic and real data indicate that the proposed strategy can outperform the competing state-of-the-art algorithms.

Deep Generative Endmember Modeling: An Application to Unsupervised Spectral Unmixing

Long-term monitoring of shoreline changes is of significant importance for coastal erosion prediction and coastal planning. This paper presents the use of the Landsat archival dataset over 29 years to monitor shoreline changes at Narrabeen–Collaroy Beach, Australia. For each scene of Landsat data, a vector-based shoreline at subpixel level was automatically extracted by employing the super-resolution border segmentation method. Monthly cross-shore beach profile surveys at five locations along the beach are used as ground truth data to assess the results. The experimental results show that after the correction of tidal effects the RMSEs of the time-series shorelines at the five locations are all less than 10 m; RMSEs of annual mean shorelines are within 5.7 m. These results were achieved within the context that the Narrabeen–Collaroy Beach has been observed to vary in width by up to 80 m during this same period. In addition, the observed variabilities in shoreline change at different locations along the 3.6-km long embayment are also clearly observed from Landsat-derived results. The results indicate the feasibility of Landsat data for long-term shoreline change monitoring.

Automatic super-resolution shoreline change monitoring using Landsat archival data: a case study at Narrabeen-Collaroy Beach, Australia

The subpixel mapping technique can specify the spatial distribution of different categories at the subpixel scale by converting the abundance map into a higher resolution image, based on the assumption of spatial dependence. Traditional subpixel mapping algorithms only utilize the low-resolution image obtained by the classification image downsampling and do not consider the spectral unmixing error, which is difficult to account for in real applications. In this paper, to improve the accuracy of the subpixel mapping, an adaptive subpixel mapping method based on a maximum a posteriori (MAP) model and a winner-take-all class determination strategy, namely, AMCDSM, is proposed for hyperspectral remote sensing imagery. In AMCDSM, to better simulate a real remote sensing scene, the low-resolution abundance images are obtained by the spectral unmixing method from the downsampled original image or real low-resolution images. The MAP model is extended by considering the spatial prior models (Laplacian, total variation (TV), and bilateral TV) to obtain the high-resolution subpixel distribution map. To avoid the setting of the regularization parameter, an adaptive parameter selection method is designed to acquire the optimal subpixel mapping results. In addition, in AMCDSM, to take into account the spectral unmixing error in real applications, a winner-take-all strategy is proposed to achieve a better subpixel mapping result. The proposed method was tested on simulated, synthetic, and real hyperspectral images, and the experimental results demonstrate that the AMCDSM algorithm outperforms the traditional subpixel mapping methods and provides a simple and efficient algorithm to regularize the ill-posed subpixel mapping problem.

/pdf/an-adaptive-subpixel-mapping-method-based-on-map-model-and-1v0w6fnvaq.pdf

An Adaptive Subpixel Mapping Method Based on MAP Model and Class Determination Strategy for Hyperspectral Remote Sensing Imagery

Mixed pixels are widely existent in remote-sensing imagery. Although the proportion occupied by each class in mixed pixels can be determined by spectral unmixing, the spatial distribution of classes remains unknown. Sub-pixel mapping SPM addresses this problem and a sub-pixel/pixel spatial attraction model SPSAM has been introduced to realize SPM. However, this algorithm fails to adequately consider the correlation between sub-pixels. Consequently, the SPM results created by SPSAM are noisy and the accuracy is limited. In this article, a method based on particle swarm optimization is proposed as post-processing on the SPM results obtained with SPSAM. It searches the most likely spatial distribution of classes in each coarse pixel to improve the SPSAM. Experimental results show that the proposed method can provide higher accuracy and reduce the noise in the results created by SPSAM. When compared with the available modified pixel-swapping algorithm, the proposed method often yields higher accuracy results.

Particle swarm optimization-based sub-pixel mapping for remote-sensing imagery

Integration of spatial attractions between and within pixels for sub-pixel mapping

Spectral unmixing is one of the important techniques for hyperspectral data processing. The analysis of spectral mixing is often based on a linear, fully constrained (FC) (i.e., nonnegative and sum-to-one mixture proportions), and least squares criterion. However, the traditional iterative processing of FC least squares (FCLS) linear spectral mixture analysis (LSMA) (FCLS-LSMA) is of heavy computational burden. Recently developed geometric LSMA methods decreased the complexity to some degree, but how to further reduce the computational burden and completely meet the FCLS criterion of minimizing the unmixing residual needs to be explored. In this paper, a simple distance measure is proposed, and then, a new geometric FCLS-LSMA method is constructed based on the distance measure. The method is in line with the FCLS criterion, free of iteration and dimension reduction, and with very low complexity. Experimental results show that the proposed method can obtain the same optimal FCLS solution as the traditional iteration-based FCLS-LSMA, and it is much faster than the existing spectral unmixing methods, particularly the traditional iteration-based method.

Geometric Method of Fully Constrained Least Squares Linear Spectral Mixture Analysis

Endmember extraction (EE) is a prerequisite task for spectral analysis of hyperspectral imagery. In all kinds of EE algorithms, maximum simplex volume-based ones, such as simplex growing algorithm (SGA) and N-FINDR algorithm, have been widely used for their fully automated and efficient performance. However, implementation of the algorithms needs dimension reduction of original data, and the algorithms include innumerable volume calculation. This leads to a low speed of the algorithms and thus becomes a limitation to their applications. In this paper, a simple distance measure is presented, and then, fast SGA and fast N-FINDR algorithm are constructed based on a proposed distance measure, which is free of dimension reduction and makes use of distance measure instead of volume evaluation to speed up the algorithm. The complexity of the proposed methods is compared with the original algorithms by theoretical analysis. Experiments show that the implementation of the two improved EE algorithms is much faster than that of the two original maximum simplex volume-based EE algorithms.

Fast Implementation of Maximum Simplex Volume-Based Endmember Extraction in Original Hyperspectral Data Space

In this paper, a new sub-pixel mapping algorithm is proposed based on sub-pixel/sub-pixel spatial attraction model (SSSAM). Different from the original sub-pixel/pixel spatial attraction model (SPSAM), the SSSAM considers the spatial distribution of each sub-pixel within neighbor pixels, when calculating the spatial attractions for sub-pixels within the centre pixel. Then the attractions are used to determine the class values of these sub-pixels. Two experiments on three artificial images and one real remote sensing image are processed. Both of the results show that compared with traditional SPSAM, the proposed method can produce sub-pixel mapping results with higher accuracy.

Sub-pixel mapping based on sub-pixel to sub-pixel spatial attraction model

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