Algorithm 1. Adopted PGD method for colored MPM application.

1:given: iterations K, data b, estimate of noise standard deviation $\delta$, stopping condition for discrepancy principle $\eta$, particle type matrix $Q$, cone projection operator for particle types ${\mathcal{P}}_{+}^Q$. 2:initialize forward operator $A$, particle distribution x. 3:for k = 1 to K do. 4:$\left[x_{k+1},y_{k+1}\right]={\mathcal{P}}_{+}^Q(x_k+{\Vert A\Vert }_2^{-2}{A}^T\left(b-A{x}_k\right))$ 5:if$\frac{\Vert A{x}_{k+1}-{b\Vert }_2}{\delta }\le \eta then$ 6:return$y_{k+1}$ 7:end if 8:end for 9:return$y_{k+1}$