&lt;title&gt;RBI-EMML signal separation for imaging techniques&lt;/title&gt;

Meidunas, Eduardo C.; Puetz, Angela M.; Hoke, Michael L.; Byrne, Charles

doi:10.1117/12.478760

Cited by 3 publications

(13 citation statements)

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“…That is w~N(0,σ 2 I) where I is the m×m identity matrix and σ 2 is the noise variance. The maximum likelihood estimate of x based on b is then given by (2) where x is the estimate of x, and || || 2 is the Euclidean norm.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…In this context, the abundance estimation can be reformulated as follows A distance function that will lead to the unmixing algorithm presented by [2] is the Kullback-Leibler distance function or Cross-Entropy, derived from Shannon's Entropy using the Bregman function formalism [12]. The reader is referred to [12] for more information on Bregman's functions and distances.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…The recent paper [2] considered the use of the so-called EMML and RBI-EMML algorithms, developed for the maximum likelihood reconstruction of emission tomography images [3,4], to solve the unmixing problem. These algorithms have the advantage of producing abundance estimates that meet positivity as well as, with proper scaling, sum-to-one constraints that the abundances need to meet.…”

Section: Introductionmentioning

confidence: 99%

“…The main focus of that work was the RBI-EMML [4] algorithm because of its significantly faster convergence rate when compared to the original EMML algorithm [3]. Simulation results presented in [2] showed that the RBI-EMML took about three orders of magnitude fewer iterations (from hundreds of thousand to hundreds) than EMML for the same problem. The derivation of the EMML approach for unmixing presented in [2] is based on a manipulation of Bayes' theorem, which was originally proposed in [5].…”

Section: Introductionmentioning

confidence: 99%

“…Simulation results presented in [2] showed that the RBI-EMML took about three orders of magnitude fewer iterations (from hundreds of thousand to hundreds) than EMML for the same problem. The derivation of the EMML approach for unmixing presented in [2] is based on a manipulation of Bayes' theorem, which was originally proposed in [5]. Here, we take a different approach by looking at the unmixing problem as a constrained prediction error minimization problem where the error between the measured spectra and its prediction by the endmembers is minimized by minimizing a distance (or generalized distance) metric.…”

Section: Introductionmentioning

confidence: 99%

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Iterative algorithms for unmixing of hyperspectral imagery

Vélez-Reyes¹,

Puetz

HOKE

et al. 2003

SPIE Proceedings

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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

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Section: Parameter Estimationmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Iterative algorithms for unmixing of hyperspectral imagery

Vélez-Reyes¹,

Puetz

HOKE

et al. 2003

SPIE Proceedings

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Retrieval of sub-pixel snow cover information in the Himalayan region using medium and coarse resolution remote sensing data

Mishra

Negi

Rawat

et al. 2009

International Journal of Remote Sensing

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A unified treatment of some iterative algorithms in signal processing and image reconstruction

2003

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Let T be a (possibly nonlinear) continuous operator on Hilbert space H. If, for some starting vector x, the orbit sequence {T k x, k = 0, 1, . . .} converges, then the limit z is a fixed point of T ; that is, T z = z. An operator N on a Hilbert space H is nonexpansive (ne) if, for each x and y in H, N x − N y x − y . Even when N has fixed points the orbit sequence {N k x} need not converge; consider the example N = −I , where I denotes the identity operator. However, for any α ∈ (0, 1) the iterative procedure defined by x k+1 = (1 − α)x k + α N x k converges (weakly) to a fixed point of N whenever such points exist. This is the Krasnoselskii-Mann (KM) approach to finding fixed points of ne operators.A wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iterative procedure,for particular choices of the ne operator N. These include the Gerchberg-Papoulis method for bandlimited extrapolation, the SART algorithm of Anderson and Kak, the Landweber and projected Landweber algorithms, simultaneous and sequential methods for solving the convex feasibility problem, the ART and Cimmino methods for solving linear systems of equations, the CQ algorithm for solving the split feasibility problem and Dolidze's procedure for the variational inequality problem for monotone operators.

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<title>RBI-EMML signal separation for imaging techniques</title>

Cited by 3 publications

References 4 publications

Iterative algorithms for unmixing of hyperspectral imagery

Iterative algorithms for unmixing of hyperspectral imagery

Retrieval of sub-pixel snow cover information in the Himalayan region using medium and coarse resolution remote sensing data

A unified treatment of some iterative algorithms in signal processing and image reconstruction

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