When a bearing appears cracked or pitted, twin impulse signals can be generated that overlap at initial faults. It was difficult to extract the atoms that best match the twin impulses based on the common maximum gaussianity criterion through traditional sparse decomposition. First, the relationship between time-frequency factors and the distance of twin impulses was discussed, according to which the optimal neighborhood could be constructed and a new method of the neighbor orthogonal matching pursuit could be introduced. In each iteration of this method, a sub-frame was constructed, consisting of the atoms neighboring the atom that had the maximum inner product with the residual signal. Next, the representation in this sub-frame was obtained, and the next residual signal was computed. The next iteration was made until the termination condition was met. The simulation and fault proved the effectiveness of this method in extracting the twin impulses and identifying the type of fault.