$m=3$. Given the number of materials and channels, random attenuation spectra are generated by assigning a random number $\mu(s,E_c) \sim \mathcal{U}(0,1)$ for each channel-material combination, where $s \in \{1,\ldots,m\}$ and $E_c \in \{E_1,\ldots, E_C\}$. With this way of generating spectra no dependencies between channels are established. Note that in most practical applications such dependencies do exist, as materials all have their own attenuation spectrum. For each phantom, reconstructions are made. The reference values for the tomographic setup and the parameter values of the MC-DART reconstruction algorithm for these reconstructions are summarized in Table \[tab:Parameters\]. For multi-channel segmentation the method as described in Section \[sec:MCDART\] is used.

We vary the number of channels $C \in\{1,\ldots,10\}$ and materials $m \in \{2,\ldots,10\}$ independently. For each combination, a random phantom $\vec{y}_{\text{init}}$ is created, after which data $\vec{P}$ is generated by applying the forward projection as described in Section \[sec:Problems\] on the phantom by applying $\mu$ and $\vec{W}$ on $\vec{y}_{\text{init}}$. In all experiments parallel-beam geometries are used and the detector size is $128$ pixels. After this, the MC-DART algorithm as described in Section \[sec:MCDART\] is applied with $K=10$ MC-DART iterations. The final segmentation is compared to the original phantom and the pixel error is computed, 