Classically, one considers the absolute Galois group G of a complete discrete valuation field K whose residue field is perfect, which is known to admit a decreasing filtration by ramification groups. If the residue field of K is not perfect, it is still possible to define analogous filtrations of G. In this talk, I will examine Abbes and Saito's construction of such a filtration in the general case, and show how to recover the classical ramification filtration if the residue field is perfect.