The low coherence of the supercontinuum (SC) generated using picosecond pump pulses is a major drawback of such SC generation scheme. In this paper, we propose to first self-similarly compress a high power picosecond pump pulse by injecting it into a nonlinearity increasing fiber. The compressed pulse is then injected into a non-zero dispersion-shifted fiber (NZ-DSF) for SC generation. The nonlinearity increasing fiber can be obtained by tapering a large mode area photonic crystal fiber. The fiber nonlinearity is varied by varying the pitch sizes of the air holes. By using the generalized nonlinear Schrödinger equation, we show that a 1 ps pump pulse with random noise can be compressed self-similarly down to a pulse width of 53.6 fs with negligible pedestal. The noise level of the compressed pulse is reduced at the same time. The 53.6 fs pulse can then be used to generate highly coherent SC in an NZ-DSF. By using the proposed scheme, the tolerance of noise level for highly coherent SC generation with picosecond pump pulses can be improved by 5 order of magnitude.