To address the issue of slowly varying broadband background noise and channel effects caused by vibration of the target in laser-coherent speech detection, this paper proposes a speech enhancement method for specific speakers based on an analysis-resynthesis framework. This method first extracts the features from the observed signal: pitch, voiced speech probability, and MCEP coefficients, where MCEP coefficients represent the spectral envelope features which can capture the shape of the spectral envelope. A GMM trained by speech features of the corresponding speaker is used to help estimate the spectral envelope features of the clean speech from the spectral envelope features of the observed speech, and then the speech signal is resynthesized by combining it with pitch and voiced speech probability estimated from the observed speech to achieve speech enhancement. The estimation of noise and channel parameters is achieved by adaptation, which maximize the posterior probability of the observed speech′s spectral envelope features, and then the estimation of the clean speech spectral envelope features is obtained by MMSE estimation. Both synthesized signal experiments and actual signal acquisition experiments verify the denoising and equalization capabilities of the algorithm in laser coherent speech detection scenarios.