The convex divergence is used as a surrogate function for obtaining a class of ICA algorithms (Independent Component Analysis) called the f-ICA. The convex divergence is a super class of α-divergence, which is a further upper family of Kullback-Leibler divergence or mutual information. Therefore, the f-ICA contains the α-ICA and the minimum mutual information ICA. In addition to theoretical interest of generalization, the f-ICA contains a subset faster than the minimum mutual information ICA. It is found that this speed control is equivalent to the α-ICA. Finally, applications to brain fMRI map’s distillation is presented.