The Radon transform (RT) plays an important role in seismic data processing for its ability to focus seismic events in the transform domain. The band-limited nature of seismic events due to the blurring effects of the source wavelet, however, causes a decrease in the temporal resolution of the transform. We have developed the deconvolutive RT (DecRT) as a generalization of conventional RT and to increase the temporal resolution. Unlike the conventional counterpart, the new basis functions can take an arbitrary shape in the time direction. This method is thus proposed to adaptively infer the temporal wave shape from the input data while finding a sparse representation of it. The new transform significantly improves the sparsity and thus the temporal resolution of the resulting seismic data. The applicability of the hyperbolic DecRT in seismic data processing is demonstrated for random noise attenuation, primary and multiple separation, high-quality stacking, and automatic velocity model building. The results obtained on synthetic and field data sets confirm the effectiveness of the method in improving the time and slowness/curvature resolutions compared with conventional transforms, which leads to improved seismic processing results in the deconvolutive Radon domains.