In this talk, I introduce two effective approaches for seimic attenuation compensation, i.e., inversion framework with L1−2 minimization and Q-RTM with adaptive stabilization scheme. Compared to conventional L1 metric, our proposed L1−2 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 cuQ-RTM, which aims to achieve an efficient, storage-saving and stable Q-RTM.