In this talk, I introduce two effective approaches for seimic attenuation compensation, i.e., inversion framework with $L_{1-2}$ minimization and $Q$-RTM with adaptive stabilization scheme. Compared to conventional $L_1$ metric, our proposed $L_{1−2}$ penalty has potential to recover exact sparse reflectivity series from noisy attenuated seismograms (kernel matrix is severely ill-conditioned). Compared to conventional low-pass filtering, our proposed stabiliza- tion scheme exhibits superior properties of time-variance and $Q$-dependence. I also present a CUDA-based code package named cu$Q$-RTM, which aims to achieve an efficient, storage-saving and stable $Q$-RTM.