This paper presents a full algorithm to compute the solution for the unsupervised unmixing problem based on
the positive matrix factorization. The algorithm estimates the number of endmembers as the rank of the matrix.
The algorithm has an initialization stage using the SVD subset selection algorithm. Testing and validation with
real and simulated data show the effectiveness of the method. Application of the approach to environmental
remote sensing is shown.
The authors proposed in previous papers the use of the constrained Positive Matrix Factorization (cPMF) to perform unsupervised unmixing of hyperspectral imagery. Two iterative algorithms were proposed to compute the cPMF based on the Gauss-Seidel and penalty approaches to solve optimization problems. Results presented in previous papers have shown the potential of the proposed method to perform unsupervised unmixing in HYPERION and AVIRIS imagery. The performance of iterative methods is highly dependent on the initialization scheme. Good initialization schemes can improve convergence speed, whether or not a global minimum is found, and whether or not spectra with physical relevance are retrieved as endmembers. In this paper, different initializations using random selection, longest norm pixels, and standard endmembers selection routines are studied and compared using simulated and real data.
This paper presents a comparison of different algorithms to compute the constrained positive matrix factorization and their application to the unsupervised unmixing problem. We study numerical methods based on the Gauss-Newton algorithm, the Seung-Lee approach, the Gauss-Seidel algorithm, and penalty methods. Preliminary results using a Hyperion image from southwestern Puerto Rico presented. Algorithms will be compared in terms of their convergence performance, and quality of the results.
This paper presents an approach for simultaneous determination of endmembers and their abundances in hyperspectral imagery unmixing using a constrained positive matrix factorization (PMF). The algorithm presented here solves the constrained PMF using Gauss-Seidel method. This algorithm alternates between the endmembers matrix updating step and the abundance estimation step until convergence is achieved. Preliminary results using a subset of a HYPERION image taken in SW Puerto Rico are presented. These results show the potential of the proposed method to solve the unsupervised unmixing problem.
This paper presents an approach for simultaneous determination of endmembers and their abundances in hyperspectral imagery using a constrained positive matrix factorization. The algorithm presented here solves the constrained PMF by formulating it as a nonnegative least squares problem where the cost function is expanded with a penalty term to enforce the sum to one constraint. Preliminary results using simulated and AVIRIS-Cuprite data are presented. These results show the potential of the method to solve the unsupervised unmixing problem.
Hyperspectral imagery provides high spectral and spatial resolution that can be used to discriminate between object and clutter occurring in subsurface remote sensing for applications such as environmental monitoring and biomedical imaging. We look at using a noncausal auto-regressive Gauss-Markov Random Field (GMRF) model to model clutter produced by a scattering media for subsurface estimation, classification, and detection problems. The GMRF model has the advantage that the clutter covariance only depends on 4 parameters regardless of the number of bands used. We review the model and parameter estimation methods using least squares and approximate maximum likelihood. Experimental and simulation model identification results are presented. Experimental data is generated by using a subsurface testbed where an object is placed in the bottom of a fish tank filled with water mixed with TiO2 to simulate a mild to high scattering environment. We show that, for the experimental data, least square estimates produce good models for the clutter. When used in a subsurface classification problem, the GMRF model results in better broad classification with loss of some spatial structure details when compared to spectral only classification.
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