The principle of speech enhancement and the method of extracting speech signals from strong noise background are introduced. Three kinds of speech intensifying algorithms based on spectrum subtraction algorithm, wiener filtering and wavelet transform, respectively, are comparatively studied. However, the two purposes of the speech enhancement algorithms, to enhance articulation and to enhance the understandability, are not related each other, and even in contradiction sometimes. Therefore, a good speech enhancement algorithm is in fact a compromise between the two purposes according to the requirement of application. In this paper, results of numerical experiment of the three algorithms are compared and studied. The results demonstrate that the speech enhancement algorithm using wavelet ransform is more efficient than the others.