Speech enhancement is widely used as a front-end to improve the speech quality in many audio systems, while it is hard to extract the target speech in multi-talker conditions without prior information on the speaker identity. It was shown that the auditory attention on the target speaker can be decoded from the electroencephalogram (EEG) of the listener implicitly. In this work, we therefore propose a novel end-to-end brain-assisted speech enhancement network (BASEN), which incorporates the listeners' EEG signals and adopts a temporal convolutional network together with a convolutional multi-layer cross attention module to fuse EEG-audio features. Considering that an EEG cap with sparse channels exhibits multiple benefits and in practice many electrodes might contribute marginally, we further propose two channel selection methods, called residual Gumbel selection and convolutional regularization selection. They are dedicated to tackling training instability and duplicated channel selections, respectively. Experimental results on a public dataset show the superiority of the proposed BASEN over existing approaches. The proposed channel selection methods can significantly reduce the amount of informative EEG channels with a negligible impact on the performance.