In this paper, we introduce a generalized velocity-dependent (VD)-seislet transform, a new domain for analyzing prestack reflection data in the CMP domain. The new transform could compress reflection data away from missing data. The nonhyperbolic NMO equation serves as a bridge between local slopes and scanned parameters that are not sensitive to data gap and aliasing. As examples, we applied the generalized VD-seislet transform in interpolating missing data under the new modified Bregman iteration framework to synthetic and field data. We expect the generalized VD-seislet transform to provide better compression ability for nonhyperbolic reflection events away from interference of missing traces. The current generalized VD-seislet transform based on equation 5 only works for CMP gathers in structurally simple areas. For structurally complex areas, OC-seislet transform (Liu and Fomel, 2010) can perform well but at the expense of high computation cost.