Iterative algorithms for unmixing of hyperspectral imagery

Abstract

This paper addresses the use of multiplicative iterative algorithms to compute the abundances in unmixing of hyperspectral pixels. The advantage of iterative over direct methods is that they allow incorporation of positivity and sum-to-one constraints of the abundances in an easy fashion while also allowing better regularization of the solution for the ill-conditioned case. The derivation of two iterative algorithms based on minimization of least squares and Kulback-Leibler distances are presented. The resulting algorithms are the same as the ISRA and EMML algorithms presented in the emission tomography literature respectively. We show that the ISRA algorithm and not the EMML algorithm computes the maximum likelihood estimate of the abundances under Gaussian assumptions while the EMML algorithm computes a minimum distance solution based on the Kulback-Leibler generalized distance. In emission tomography, the EMML computes the maximum likelihood estimate of the reconstructed image. We also show that, since the unmixing problem is in general overconstrained and has no solutions, acceleration techniques for the EMML algorithm such as the RBI-EMML will not converge. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/20/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Proc. of SPIE Vol. 5093 419 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/20/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

Unsupervised unmixing of hyperspectral imagery using the constrained positive matrix factorization

“…A direct solution no longer exists when the positive constraints are enforced [3,4]. The linear least squares problem with positive constraints is referred in the linear algebra literature as the non-negative linear least squares problem (NNLS) for which Lawson and Hanson's Algorithm [3] is the most commonly used to compute a solution.…”

“…Other iterative algorithms can be used to solve the NNLS. Multiplicative iterative algorithms to solve the NNLS and its application to positively constrained unmixing are discussed in [4].…”

“…(1) where, in the ideal case, pixels are enclosed in a simplex whose corners are the endmembers. The geometrical mixing model provides an intuitive mean to describe the endmember determination problem which is reduced to determine the corners of the simplex that encloses the data cloud [1,4,5]. Figure 3 shows examples of simplex in two dimensions.…”

An FPGA implementation of image space reconstruction algorithm for hyperspectral imaging analysis

“…This problem is known as the unmixing problem. 8,9 Mixed pixels are caused by a low spatial resolution of HSI sensor or as a result of different materials combined in a homogeneous mixture 8 Pixel unmixing has important applications such as object quantification, mineral identification, plants health, automatic materials detection, and others. 8,10 In addition, it can be used to generate a training set for image classification.…”

“…9 ISRA is a supervised classification method. These means a priory information of the endmembers is known.…”