none5noA novel signal compression and reconstruction procedure suitable for guided wave based structural health monitoring (SHM) applications is presented. The proposed approach combines the wavelet packet transform and frequency warping to generate a sparse decomposition of the acquired dispersive signal. The sparsity of the signal in the considered representation is exploited to develop data compression strategy based on the Best-Basis Compressive sensing (CS) theory. The proposed data compression strategy has been compared with the transform encoder based on the Embedded Zerotree (EZT), a well known data compression algorithm. These approaches are tested on experimental Lamb wave signals obtained by acquiring acoustic emissions in a 1m^2...