Blind source separation (BSS) algorithms based on the noise free model are not applicable when the SNR is low. To deal with this issue, one way is to denoise the mixtures corrupted by white Gaussian noise, firstly, and then utilize the BSS algorithms. Therefore, a Waveshrink algorithm is proposed based on translation invariant to denoise mixtures with strong noise. The high frequency coefficients sliding window method is utilized to estimate the noise variance accurately, and Bayesshrink algorithm is utilized for a more reasonable threshold. Consequently, the scope of the translation invariant is narrowed without degrading the performance of denoising, thus reducing the computation amount. Simulation results indicate that the proposed approach perform better in denoising compared with the traditional Waveshrink algorithm, and can remarkably enhance the separation performance of BSS algorithms, especially in the case with low signa.