quantum mechanics - How to decompose a density matrix of a mixed ensemble into a sum of pure ensembles

I'm trying to solve a problem where I am given a few matrices and asked to determine if they could be density matrices or not and if they are if they represent pure or mixed ensembles. In the case of mixed ensembles, I should find a decomposition in terms of a sum of pure ensembles. The matrix I'm having trouble with is this one

$$ \rho = \left[\begin{array}{ccc}\frac{1}{2} & 0 & \frac{1}{4} \\ 0 & \frac{1}{4} & 0 \\ \frac{1}{4} & 0 & \frac{1}{4}\end{array}\right] $$

I know it's a mixed ensemble density matrix because $\mathrm{Tr}(\rho^2)<1$, but how can I decompose if I don't even know how big is this sum? I mean, any number of pure states may compose a mixed ensemble since they do not need to be orthogonal. How can I approach this?