5 Comparison methods

Many experiments were carried out with these algorithms. For each one we got mixing and demixing matrices and image sources. Even though a visual appreciation of the resulting sources was informative, a quantitative quality measurement was needed.

The source filters.

The spectrum at pixel location (k,l) is called $S(k,l,\lambda)$, $\lambda$ being the wavelength. Each image X_i(k,l) is observed with a filter of transmission profile $T_i(\lambda)$. We have:

$$% X_i(k,l)=\int T_i(\lambda)S(k,l,\lambda){\rm d}\lambda.$$ (11)

Let us call c(i,j) the demixing coefficient of source j for image i, source S_j(k,l) is written as:

$$% S_j(k,l)=\sum_i c(i,j)X_i(k,l).$$ (12)

Eqs. (11) and (12):

$$% S_j(k,l)=\int \left(\sum_i c(i,j) T_i(\lambda)\right)S(k,l,\lambda){\rm d}\lambda.$$ (13)

We can write:

$$% S_j(k,l)=\int U_j(\lambda) S(k,l,\lambda){\rm d}\lambda$$ (14)

with:

$$% U_j(\lambda)=\sum_i c(i,j) T_i(\lambda).$$ (15)

The sources can be considered as the observed images through filters $U_j(\lambda)$, which are called the source filters. For each BSS we display the set of its source filters.

The energy break-down.

From each BSS, the image energy coming from a given source was evaluated. Then we can compute the energy related to each source from all the images. This criterion allows us to classify the sources by decreasing energy.

Source visualization.

The source images are displayed in order to optimize the contrast. That allows us to compare the different sources in the best contrast conditions. This visual comparison was essential to select the best identification, but it is too qualitative.