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An algorithm is developed in the time-frequency domain. It is assumed that the transfer function can be estimated only under the condition that the approximation signal is inactive. The algorithm uses a deep neural network trained on the mixed signal to detect the activity of the approximation signal, and the conventional frequency domain least squares method is used to estimate the acoustic wave transfer function without detecting any active frequencies. For the incomplete problem of the proposed transfer function (ITF) estimation, the algorithm is completed by the most sparse representation of the ITF in the fuzzy time domain. The soft threshold function is applied to the time domain, adaptively completed by the soft threshold function, and oversampling is used to improve the accuracy. . The experimental results show that the algorithm converges by about 50% faster than the traditional algorithm when the active frequency is 80%. In the speech experiment, the improved ADMM algorithm takes 0.125s, which is obviously superior to the traditional algorithm. It provides a new idea for the problem of echo cancellation in voice transmission services.