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David Youssefi
otb
Commits
e12a3e96
Commit
e12a3e96
authored
13 years ago
by
Manuel Grizonnet
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DOC:update mdmd doxygen
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53e38d5a
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Code/Hyperspectral/otbMDMDNMFImageFilter.h
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Code/Hyperspectral/otbMDMDNMFImageFilter.h
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e12a3e96
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@@ -31,7 +31,7 @@ namespace otb
* \brief This filter implements unmixing based non negative matrix factorization (NMF) which
* finds simultaneously the end members and abundances matrix which
* product is the closer to the observed data, based on the following
* works:
* works:
* K. S. F.J. Theis and T. Tanaka, First results on uniqueness of
sparse non-negative matrix factorisation.
* M. G. A. Huck and J. Blanc-Talon, IEEE TGRS, vol. 48, no. 6, pp. 2590-2602, 2010.
...
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@@ -68,7 +68,7 @@ namespace otb
* error :
* \f$ RQE({\mathbf A}, {\mathbf S})=\|\mathbf R-{\mathbf A} {\mathbf S}\|^2_F \f$. In order to
* satisfy the sum-to-one constraint for hyperspectral data, a
* regularization term \f$ STU(\mathbf S) \f$ can be added to the objective
* regularization term \f$ STU(
{
\mathbf S
}
) \f$ can be added to the objective
* function.
*
* A generic expression for the optimized function is \f$
...
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@@ -97,13 +97,13 @@ namespace otb
* on multiplicative rules, or else alternate gradient descent
* iterations, or else on alternate least square methods. In MDMD-NMF, the update rules
* at each iteration become :
* \f$ \begin{
eqnarray
}
*
\label{algomdmd}
\mathbf S&\leftarrow &P\left [\mathbf S-\mu_S \left( \bar \mathbf A^T
* \f$ \begin{
tabular
}
* \mathbf S&\leftarrow &P\left [\mathbf S-\mu_S \left( \bar \mathbf A^T
* (\bar\mathbf A\mathbf S-\bar\mathbf R)-\lambda_S(\mathbf S-\frac{1}{J}\1_{JI})\right)\right
* ]\\ \nonumber \mathbf A &\leftarrow &P\left [\mathbf A-\mu_A \left(
* (\mathbf A\mathbf S-\mathbf R)\mathbf S^T +\lambda_A(\mathbf A-\frac{1}{L}\ \mathbf hbf
* 1_{LL}\mathbf A)\right)\right ]
* \end{
eqnarray
} \f$
* \end{
tabular
} \f$
* where \f$ \mu_A\f$ and \f$\mu_S \f$
* are the step sizes.
* Huck propose a
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