Blind source separation (BSS) is the approach taken to estimate original source signals using only the information of the mixed signals observed in each input channel, and much attention has been paid to BSS in many fields of signal processing. Two approaches have been widely studied and employed to solve the BSS problem: one is based on independent component analysis (ICA) and the other relies on the sparseness of source signals (TF-masking). In order to speed up the convergence rate and avoid permutation problems, this paper presents a method combining the advantages of the two methods uses the results of TF masking to initialize the FDICA. This paper also proposes a new post-processing method for FDICA: Local Minimum Ratio Control (LMRC) spectral subtraction, which is based on the sparse characteristics of speech. Compared with the conventional TF masking and Wiener filter post processing methods, the proposed method can more effectively control musical noise, and improve the separation performance. Experimental results with synthetic data and real data demonstrate the effectiveness of the proposed method.