Composite　structure　is　increasingly　used　in　civil　and　aerospace　applications　due　to　its　high　mechanical　performance.　Lamb　wave　based　sparse　reconstruction　imaging　for　damage　localization　is　promising　for　structural　health　monitoring　(SHM)　and　nondestructive　evaluation　(NDE)　by　using　few　measurements.　However,　this　dictionary　based　method　requires　accurate　atoms　to　represent　Lamb　wave　propagating　features　in　structure　very　well.　Besides　dispersion,　signal　changes　caused　by　amplitude　modulation　should　be　considered　for　waveform　distortion　when　constructing　the　dictionary　for　sparse　imaging　method.　In　this　paper,　a　non-contact　laser　is　used　for　Lamb　wave　excitation　which　exhibits　a　strong　amplitude　modulation　in　low　frequency.　Additionally,　the　strong　attenuation　resulting　from　material　damping　would　also　presents　a　distance-dependent　amplitude　modulation.　To　reconstruct　an　amplitude　model　of　Lamb　wave,　the　decomposition　method　of　system　response　and　attenuation　is　proposed.　Then,　the　influence　of　amplitude　modulation　on　signal　representation　is　analyzed,　which　shows　the　restriction　of　dictionary　without　considering　amplitude　modulation.　On　this　basis,　the　amplitude　considered　dictionary　is　built　together　with　the　phase　considered　dictionary　for　sparse　imaging　in　terms　of　damage　detection.　Furthermore,　according　to　Lamb　wave　reflection　model,　the　solution　for　sparse　reconstruction　imaging　is　given.　Finally,　the　performance　of　sparse　imaging　method　is　discussed　by　experimental　investigation　with　different　parameters.　The　results　show　the　efficiency　of　the　proposed　method　with　improved　imaging　performance　and　give　comparisons　for　better　parameter　choice.　©　2018　Elsevier　B.V.