Jakob Sigurdsson

Hyperspectral Unmixing With

Hyperspectral unmixing is an important technique for analyzing remote sensing images. In this paper, we consider and examine the ℓq, 0 ≤ q ≤ 1 penalty on the abundances for promoting sparse unmixing of hyperspectral data. We also apply a first-order roughness penalty to promote piecewise smooth end-members. A novel iterative algorithm for simultaneously estimating the end-members and the abundances is developed and tested both on simulated and two real hyperspectral data sets. We present an extensive simulation study where we vary both the SNR and the sparsity of the simulated data and identify the model parameters that minimize the reconstruction errors and the spectral angle distance. We show that choosing 0 ≤ q <; 1 can outperform the ℓ1 penalty when the SNR is low or the sparsity of the underlying model is high. We also examine the effects of the imposing the abundance sum constraint using a real hyperspectral data set.

l_{q}

Hyperspectral unmixing is the process where the reflectance spectrum from a mixed pixel is decomposed into separate distinct spectral signatures (endmembers). A mixed pixel results when spectra from more than one material is recorded by a sensor in one pixel. The goal of linear unmixing is to identify the number of endmembers in an image, the endmembers themselves and their abundances in each pixel. This paper presents a new smooth method for unmixing hyperspectral images using nonnegative cyclic descent. The proposed method uses iterative cyclic descent algorithm to find the endmembers and their abundances. The algorithm uses an ℒ1 norm to promote sparseness in the abundances. Because the spectrum of the endmembers varies smoothly, a first order roughness penalty is added to discourage roughness in the endmembers. The algorithm does not use any prior information about the data. The method is tested using a real hyperspectral image of an urban landscape.

Regularization

Blind hyperspectral unmixing involves jointly estimating endmembers and fractional abundances in hyperspectral images. An endmember is the spectral signature of a specific material in an image, while an abundance map specifies the amount of a material seen in each pixel in an image. In this paper, a new cyclic descent algorithm for blind hyperspectral unmixing using total variation (TV) and ℓq sparse regularization is proposed. Abundance maps are both spatially smooth and sparse. Their sparsity derives from the fact that each material in the image is not represented in all pixels. The abundance maps are assumed to be piecewise smooth since adjacent pixels in natural images tend to be composed of similar material. The TV regularizer is used to encourage piecewise smooth images, and the ℓq regularizer promotes sparsity. The dyadic expansion decouples the problem, making a cyclic descent procedure possible, where one abundance map is estimated, followed by the estimation of one endmember. A novel debiasing technique is also employed to reduce the bias of the algorithm. The algorithm is evaluated using both simulated and real hyperspectral images.

A smooth hyperspectral unmixing method using cyclic descent

In this paper an endmember constrained semi-supervised hyperspectral unmixing method is proposed. The linear model is used to represent the hyperspectral data. A priori information about the endmembers is incorporated into the objective function with soft regularization. This information can be acquired from a spectral library or from the data itself. Quantitative evaluation of the method is done using simulated data and it is shown the soft regularization can yield better results than hard regularization. The method is also applied on a real hyperspectral data set and the estimated abundance maps improve when a priori information is used to aid the unmixing.

Blind Hyperspectral Unmixing Using Total Variation and

Hyperspectral unmixing is an important technique for analyzing hyperspectral remote sensing images. We propose an estimation algorithm that, simultaneously, encourages smoothness in the endmembers and sparseness in the abundances by using first order roughness and l0 penalties. The method is evaluated both on simulated data and a real hyperspectral image of an urban landscape.

\ell_q

Hyperspectral unmixing is the task of decomposing hyperspectral images into endmembers and their abundances. The endmembers are spectral signatures of specific material in the image and the abundances dictate the amount of the material found in each pixel. In this paper we present a blind signal separation method, based on the total variation penalty, that simultaneously estimates the endmembers and the abundances. We evaluate our method using both simulated and a real data set.

Sparse Regularization

Blind hyperspectral unmixing is the task of jointly estimating the spectral signatures of material in a hyperspectral images and their abundances at each pixel. The size of hyperspectral images are usually very large, which may raise difficulties for classical optimization algorithms, due to limited memory of the hardware used. One solution to this problem is to consider distributed algorithms. In this paper, we develop a distributed sparse hyperspectral unmixing algorithm using the alternating direction method of multipliers (ADMM) algorithm and ℓ1 sparse regularization. Each sub-problem does not need to have access to the whole hyperspectral image. The algorithm is evaluated using a very large real hyperspectral image.

Endmember constrained semi-supervised hyperspectral unmixing

Non-negative matrix factorization (NMF) has found use in fields such as remote sensing and computer vision where the signals of interest are usually non-negative. Data dimensions in these applications can be huge and traditional algorithms break down due to unachievable memory demands. One is then compelled to consider distributed algorithms. In this paper, we develop for the first time a distributed version of NMF using the alternating direction method of multipliers (ADMM) algorithm and dyadic cyclic descent. The algorithm is compared to well established variants of NMF using simulated data, and is also evaluated using real remote sensing hyperspectral data.

Smooth and sparse hyperspectral unmixing using an l 0 penalty

Principal Component Analysis (PCA) has widely been used in hyperspectral image analysis as a preprocessing step for further processing. Recently, sparse PCA methods have emerged as a powerful alternative. In this paper we propose a wavelet based sparse PCA method for hyperspectral image denoising. The proposed method is evaluated by using simulated and real data.

Smooth spectral unmixing using total variation regularization and a first order roughness penalty

Principal component analysis (PCA) and other multivariate methods have proven to be useful in a variety of engineering and science fields. PCA is commonly used for dimensionality reduction. PCA has also proven to be useful in functional magnetic resonance imaging (fMRI) research where it is used to decompose the fMRI data into components which can be associated with biological processes. In this paper we develop a smooth version of PCA derived from a maximum likelihood framework. A 1st order roughness penalty term is added to the log-likelihood function which is then maximized for the parameters of interest with an expectation maximization (EM) algorithm. This new method is applied both to simulated data and real fMRI data.