Bube and Langan (1997),
Fomel and Claerbout (1995),
with p=1, Huber (1981),
with p=1, Hugonnet (1998), and finally
Claerbout and Fomel (1999), and there is probably more.
Each weighting function has different pros and cons and should be carefully chosen according to the problem we are trying to solve. Generally speaking, they all aim to weight down outliers in the data. With only the threshold to set up a priori, the Huber solver appears far easier to utilize than IRLS algorithms. Moreover, on a velocity stack inversion problem, for a very common weighting function (equation 5) with reasonable parameters (damping factor and restart parameter), I have shown that the Huber norm fosters better convergence than IRLS.