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The simultaneous unmixing of several pixels
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| It is clear that in practice equation (1) cannot be exactly
satisfied by all pixels. So, one may introduce an error term on its
right-hand-side and write it as
wi = ai x + bi y + ci z + ei (3)
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If we consider L mixed pixels, we shall have L x K linear equations with L x N unknowns (K is the number of bands and N is the number of mixing proportions in each pixel). We can try to solve all these equations simultaneously by the least square errors method: Equation (3) can be written as: wij - ai xj - bi yj- ci zj = eij (4)
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where wij is the value of the i th pixel in the j th spectral band. The least squares error solution chooses values for ai, bi, ci,... where i=1,...,L, so that the quantity
is minimised. There are two problems with this approach: |
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