MUSE or "MUltipath Stochastic Equalization" is a new framework to integrate a stochastic HMM-like model of the clean signal within an equalization scheme where an equalization function is associated to each possible path in the model, and whose parameters are estimated using ML or MAP criteria. The advantages and limitations of this approach are discussed as well as the problems of pruning the paths and choosing the optimal path at a given moment. Three equalization functions are developed, i.e. removing a bias, linear multiple regression and spectral subtraction. Comparison of this approach with the stochastic matching approach is provided. Recognition experiments show that MUSE removing bias outperforms classical cepstral normalization and adaptive filtering for more critical recognition conditions.