Does anyone have an idea how to project onto the ell^{2,1} ball efficiently, i.e. how to solve
$$ u = \arg \min_u  \|u-f \|^2    \text{such that } \left(\sum_i \big(\sum_j |u_{i,j}|\big)^2 \right)^{1/2}$$
for a matrix $u \in \mathbb{R}^{n \times m}$ efficiently?