The　time-reversal　(TR)　technique　has　been　developed　to　solve　inverse　problems　and　to　reconstruct　sources.　However,　much　work　on　the　topic　so　far　has　not　considered　the　determination　of　source　excitation　time　instants,　which　is　a　crucial　step　toward　practical　applications　of　the　TR　method.　In　this　article,　we　introduce　the　concept　of　kurtosis　into　the　TR　process　to　reconstruct　not　only　spatial　locations　but　also　excitation　time　instants　of　the　sources.　Our　method　paves　the　way　for　extensions　and　applications　of　the　TR　method　to　real-world　problems　such　as　identifying　radiation　sources　of　different　time　in　various　environments.　Numerical　examples　are　presented　to　demonstrate　the　effectiveness　of　the　proposed　concept　and　method.