I am reading this paper where they introduce norm penalties for source separation. In table 1, the $\log/ l_1$ type is $\sum_{g} log(\epsilon + \lVert H_{g} \rVert_1)$. I wonder this $\lVert H_{g} \rVert_1$ refer to which definition of $l1$ norm? In wikipedia, it has 2 definitions for this symbol.
"Entrywise" matrix norms: $\Vert A \Vert_p = \Vert \mathrm{vec}(A) \Vert_p = \left( \sum_{i=1}^m \sum_{j=1}^n |a_{ij}|^p \right)^{1/p}$ (wiki) or
Matrix norms induced by vector norms: $ \|A\|_1 = \max_{1 \leq j \leq n} \sum_{i=1}^m | a_{ij} |$ (wiki)
which is simply the maximum absolute column sum of the matrix.
One thing is below the table, the description said ""all norms are elementwise over matrix entries". So I doubt it is the first definition but not fully understand. Very appreciate if you may add explanation why it is that type of norm.