Normal moveout (NMO) correction is routinely applied to each common-midpoint (CMP) gather before forming a stack section. Trace stretching is inherent in the conventional NMO correction, causing frequency distortion and temporal resolution degradation in the stacked image. We have developed a novel method to compute a superresolution stack directly from CMP gathers by solving an optimization problem that leads to an -norm minimization of the model based on compressive sensing principles. Our algorithm is able to recover the superposition of signals in a specialized parallel-shifted hyperbolic Radon-transform domain. The superresolution stacking result is then extracted directly from the transform domain without inversely transforming back to the time-offset domain. The effectiveness of the developed methodology in producing superresolution stack images was tested on a synthetic data set and a land data set from central Saudi Arabia. Test results clearly indicate that our method reduces the stretch effect, enhances the signal, attenuates multiples and noise, and results in a substantial improvement on the temporal and spatial resolutions of the stack image especially in regions dominated by noise.