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Additional resources for Knowledge-Based Intelligent Information and Engineering Systems: 11th International Conference, KES 2007, XVII Italian Workshop on Neural Networks, Vietri sul Mare, Italy, September 12-14, 2007, Proceedings, Part III
Four supplied classes (grit, vegetation, bricks, roads, from left to right) are shown in the top row of Fig. 3. This classiﬁcation has been Blind Source Separation Applied to Spectral Unmixing 7 Fig. 3. Top, left to right: grit, vegetation, brick, road classes associated to our test 102band hyperspectral image. Middle: four fractional endmember abundances extracted by MaxNG with L2 -distance nongaussianity measure. Bottom: four fractional endmember abundances extracted by MaxNG with squared-skewness nongaussianity measure.
3) The functions gj , i = 1, 2, 3, are known in literature as the Shulman-Herve stabilizers, and their task is preserving edges during the reconstruction . Unsupervised Blind Separation and Debluring of Mixtures of Sources 27 The regularization parameters λ2j , j = 1, 2, 3, reﬂect the conﬁdence that we have in the data whereas qj , j = 1, 2, 3, have the meaning of threshold for creating a discontinuity on their respective sources sj . In the blind problem, both the sources and the mixing matrix are unknown.
We assume that the linear operators Hi and the variance of the noise are known. Let us consider ﬁrst the non–blind problem, in which the mixing matrix A is known. Let C be the set of pairs of adjacent pixels in a vertical or in an horizontal way. A clique c is an element of C. We denote the ﬁnite diﬀerence operator of the generic vector y in the clique c by Dc y. A regularized solution is deﬁned as the minimum of the following energy function: ⎛ ⎞ 2 3 EA (s) = m i − Hi ⎝ i=1 where gj (t) = 3 aij sj ⎠ 3 + j=1 ⎧ 2 ⎨t , ⎩ j=1 if |t| < qj 2q|t| − qj2 if |t| ≥ qj , λ2j gj (Dc (sj )), (2) c∈C j = 1, 2, 3.