Lamb wave testing for structural health monitoring (SHM) often relies on analysis of wavefields recorded through scanning laser Doppler vibrometers (SLDVs) or ultrasonic scanners. Damage detection and characterization with these techniques requires isolation of defect-induced reflections in the wavefield from the injected wave packet and from scattering events associated with structural features such as boundaries, rivets, joints, etc. This is a challenging task when dealing with complex structures and multimodal, dispersive propagation regimes, whereby various wave contributions in both the time/space and the frequency/wavenumber domain overlap. A new mathematical tool named warped curvelet frames (WCFs) is proposed to effectively decompose the recorded wavefields. The presented technique results from the combination of two operators, i.e., the curvelet transform (CT) and the warped frequency transform (WFT). The CT provides an optimally sparse representation of nondispersive wave propagators. Combining the CT with the WFT allows for a flexible analysis of multimodal wave propagation in dispersive media. Exploiting the spatial and temporal localization of curvelets, as well as the spectro-temporal adaptation of the analysis frame to the characteristics of each propagating mode, provided by frequency warping, a convenient decomposition of guided waves is achieved and relevant contributions can be effectively isolated. The proposed approach is validated through dedicated simulations and further tested experimentally to demonstrate the effectiveness of the method in separating guided wave modes corresponding to acoustic events in close spatial proximity.