We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

Recent advances in airborne and spaceborne hyperspectral imaging technology have provided end users with rich spectral, spatial, and temporal information. They have made a plethora of applications feasible for the analysis of large areas of the Earth?s surface. However, a significant number of factors-such as the high dimensions and size of the hyperspectral data, the lack of training samples, mixed pixels, light-scattering mechanisms in the acquisition process, and different atmospheric and geometric distortions-make such data inherently nonlinear and complex, which poses major challenges for existing methodologies to effectively process and analyze the data sets. Hence, rigorous and innovative methodologies are required for hyperspectral image (HSI) and signal processing and have become a center of attention for researchers worldwide.

/pdf/advances-in-hyperspectral-image-and-signal-processing-a-4kxt4zjyeh.pdf

Advances in Hyperspectral Image and Signal Processing: A Comprehensive Overview of the State of the Art

Advances in computing technology have fostered the development of new and powerful deep learning (DL) techniques, which have demonstrated promising results in a wide range of applications. Particularly, DL methods have been successfully used to classify remotely sensed data collected by Earth Observation (EO) instruments. Hyperspectral imaging (HSI) is a hot topic in remote sensing data analysis due to the vast amount of information comprised by this kind of images, which allows for a better characterization and exploitation of the Earth surface by combining rich spectral and spatial information. However, HSI poses major challenges for supervised classification methods due to the high dimensionality of the data and the limited availability of training samples. These issues, together with the high intraclass variability (and interclass similarity) –often present in HSI data– may hamper the effectiveness of classifiers. In order to solve these limitations, several DL-based architectures have been recently developed, exhibiting great potential in HSI data interpretation. This paper provides a comprehensive review of the current-state-of-the-art in DL for HSI classification, analyzing the strengths and weaknesses of the most widely used classifiers in the literature. For each discussed method, we provide quantitative results using several well-known and widely used HSI scenes, thus providing an exhaustive comparison of the discussed techniques. The paper concludes with some remarks and hints about future challenges in the application of DL techniques to HSI classification. The source codes of the methods discussed in this paper are available from: https://github.com/mhaut/hyperspectral_deeplearning_review .

Deep learning classifiers for hyperspectral imaging: A review

In this paper, we present a spatial spectral hyperspectral image (HSI) mixed-noise removal method named total variation (TV)-regularized low-rank matrix factorization (LRTV). In general, HSIs are not only assumed to lie in a low-rank subspace from the spectral perspective but also assumed to be piecewise smooth in the spatial dimension. The proposed method integrates the nuclear norm, TV regularization, and $L_1$ -norm together in a unified framework. The nuclear norm is used to exploit the spectral low-rank property, and the TV regularization is adopted to explore the spatial piecewise smooth structure of the HSI. At the same time, the sparse noise, which includes stripes, impulse noise, and dead pixels, is detected by the $L_1$ -norm regularization. To tradeoff the nuclear norm and TV regularization and to further remove the Gaussian noise of the HSI, we also restrict the rank of the clean image to be no larger than the number of endmembers. A number of experiments were conducted in both simulated and real data conditions to illustrate the performance of the proposed LRTV method for HSI restoration.

Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration

Image super-resolution

Hyperspectral images (HSIs) are often degraded by a mixture of various kinds of noise in the acquisition process, which can include Gaussian noise, impulse noise, dead lines, stripes, and so on. This paper introduces a new HSI restoration method based on low-rank matrix recovery (LRMR), which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. By lexicographically ordering a patch of the HSI into a 2-D matrix, the low-rank property of the hyperspectral imagery is explored, which suggests that a clean HSI patch can be regarded as a low-rank matrix. We then formulate the HSI restoration problem into an LRMR framework. To further remove the mixed noise, the “Go Decomposition” algorithm is applied to solve the LRMR problem. Several experiments were conducted in both simulated and real data conditions to verify the performance of the proposed LRMR-based HSI restoration method.

Hyperspectral Image Restoration Using Low-Rank Matrix Recovery

Due to the low-dimensional property of clean hyperspectral images (HSIs), many low-rank-based methods have been proposed to denoise HSIs. However, in an HSI, the noise intensity in different bands is often different, and most of the existing methods do not take this fact into consideration. In this paper, a noise-adjusted iterative low-rank matrix approximation (NAILRMA) method is proposed for HSI denoising. Based on the low-rank property of HSIs, the patchwise low-rank matrix approximation (LRMA) is established. To further separate the noise from the signal subspaces, an iterative regularization framework is proposed. Considering that the noise intensity in different bands is different, an adaptive iteration factor selection based on the noise variance of each HSI band is adopted. This noise-adjusted iteration strategy can effectively preserve the high-SNR bands and denoise the low-SNR bands. The randomized singular value decomposition (RSVD) method is then utilized to solve the NAILRMA optimization problem. A number of experiments were conducted in both simulated and real data conditions to illustrate the performance of the proposed NAILRMA method for HSI denoising.

/pdf/hyperspectral-image-denoising-via-noise-adjusted-iterative-242owh1put.pdf

Hyperspectral Image Denoising via Noise-Adjusted Iterative Low-Rank Matrix Approximation

Blind hyperspectral unmixing (HU), which includes the estimation of endmembers and their corresponding fractional abundances, is an important task for hyperspectral analysis. Recently, nonnegative matrix factorization (NMF) and its extensions have been widely used in HU. Unfortunately, most of the NMF-based methods can easily lead to an unsuitable solution, due to the nonconvexity of the NMF model and the influence of noise. To overcome this limitation, we make the best use of the structure of the abundance maps, and propose a new blind HU method named total variation regularized reweighted sparse NMF (TV-RSNMF). First, the abundance matrix is assumed to be sparse, and a weighted sparse regularizer is incorporated into the NMF model. The weights of the weighted sparse regularizer are adaptively updated related to the abundance matrix. Second, the abundance map corresponding to a single fixed endmember should be piecewise smooth. Therefore, the TV regularizer is adopted to capture the piecewise smooth structure of each abundance map. In our multiplicative iterative solution to the proposed TV-RSNMF model, the TV regularizer can be regarded as an abundance map denoising procedure, which improves the robustness of TV-RSNMF to noise. A number of experiments were conducted in both simulated and real-data conditions to illustrate the advantage of the proposed TV-RSNMF method for blind HU.

Total Variation Regularized Reweighted Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing

Hyperspectral (HS) imaging, also known as image spectrometry, is a landmark technique in geoscience and remote sensing (RS). In the past decade, enormous efforts have been made to process and analyze these HS products, mainly by seasoned experts. However, with an ever-growing volume of data, the bulk of costs in manpower and material resources poses new challenges for reducing the burden of manual labor and improving efficiency. For this reason, it is urgent that more intelligent and automatic approaches for various HS RS applications be developed. Machine learning (ML) tools with convex optimization have successfully undertaken the tasks of numerous artificial intelligence (AI)-related applications; however, their ability to handle complex practical problems remains limited, particularly for HS data, due to the effects of various spectral variabilities in the process of HS imaging and the complexity and redundancy of higher-dimensional HS signals. Compared to convex models, nonconvex modeling, which is capable of characterizing more complex real scenes and providing model interpretability technically and theoretically, has proven to be a feasible solution that reduces the gap between challenging HS vision tasks and currently advanced intelligent data processing models.

Wei He

Papers

Hyperspectral Image Restoration Using Low-Rank Matrix Recovery

Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration

Hyperspectral Image Denoising via Noise-Adjusted Iterative Low-Rank Matrix Approximation

Total Variation Regularized Reweighted Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing

Interpretable Hyperspectral Artificial Intelligence: When nonconvex modeling meets hyperspectral remote sensing