The　finite　rate　of　innovation(FRI)　samples　signal　at　rate　of　sub-Nyquist　rate　by　using　the　known　waveform　structure,　which　has　a　wide　application　prospect　in　wideband　information　systems.　However,　in　the　real-world　information　system,　the　signal　waveform　structure　is　often　distorted　by　the　non-ideal　factors,　such　as　noise　and　long-distance　transmission,　which　leads　to　fail　to　reconstruct　the　FRI　waveform.　According　to　the　principle　of　waveform　regeneration,　an　FRI　reconstruction　method　based　on　long　and　short-term　memory(LSTM)　is　proposed　in　this　paper.　This　method　replaces　the　sampling　kernel　of　FRI　sampling　system　by　an　automatic　LSTM　encoder,　and　the　distorted　waveform　with　unknown　structure　is　obtained　by　off-line　training.　Thus,　the　waveform　sequence　is　projected　to　a　Dirac　signature　sequence.　The　FRI　sampling　and　reconstruction　of　waveform　distortion　signal　are　realized.　The　results　show　that　the　proposed　method　can　effectively　reconstruct　the　FRI　signals,　which　distorted　by　the　multipath　effect,　by　exploiting　the　standard　annihilating　filter.　©　2022,　Chinese　Institute　of　Electronics.　All　right　reserved.