Absorption in subsurface media greatly reduces the resolution of seismic data. Absorption not only dissipates the high-frequency components of the wave, but it also distorts the seismic wavelet. The inverse -filtering method is an effective method to correct the attenuation and dispersion of the seismic wave. We evaluated an absorption compensation method based on -norm regularization. Forward modeling in the absorption medium is described by a Fredholm integral equation in the time domain, and the absorption compensation comes down to solving the Fredholm integral equation. The solutions of the Fredholm integral equation are extremely unstable. Generally, -norm regularization can be used to seek stable solutions of the Fredholm integral equation, but it makes the solutions smooth and reduces the resolution of seismic data. We used -norm regularization to overcome instability of solving the integral equation; it makes the solutions have a higher resolution than -norm regularization. The iteratively reweighted method is used to solve the minimization problem. Tests on synthetic and real data examples showed that the absorption compensation method that we evaluated can effectively correct the attenuation and dispersion of the seismic wave.