We have developed and applied an inverse -filter formulation using synchrosqueezed wavelet transforms for the compensation of attenuating and dispersive media. A damping criterion concerning the reconstruction of the effective components for controlling noise amplification and the separation of the noise and signal in the synchrosqueezed wavelet domain is generated. The proposed method provides stable attenuation compensation without decreasing the seismic vertical and lateral resolution. The best property of the proposed method, unlike conventional inverse -filtering methods, is that it carries out amplitude compensation for the effective components located at some time samples in the time-frequency domain. The spectral reconstruction contributes to the reconstruction of the trace in the time domain and suppresses the ambient noise located at high frequencies at later times, especially suppressing the ambient noise within the main frequency band. It is not a noise-level-dependent method. We validated our approach with synthetic and real data. The comparison of the proposed method with the conventional stabilized inverse -filtering method is also carried out to illustrate the particular features of the proposed method. The examples demonstrate that our proposed method can effectively compensate for the amplitude attenuation by suppressing the ambient noise and further provide seismic images at high resolution while highlighting the effective details. Furthermore, it is a robust and easily tunable algorithm.