Terahertz　(THz)　time-domain　detection　has　emerged　as　a　promising　tool　for　nondestructive　testing　due　to　its　superior　detection　accuracy　and　sensitivity　for　both　interfaces　and　internal　defects　inside　non-metallic　materials.　In　THz　nondestructive　evaluation,　accurate　characterizations　of　time-of-flight　(TOF)　extracted　from　the　echo　signal　are　critical　to　locate　the　layer　interfaces　and　damages　inside　the　structure.　However,　for　prevalent　complex　THz　echo　signals　such　as　overlapping　echoes,　low　signal-to-noise　(SNR)　echoes　and　severe　dispersion　echoes,　conventional　methods　by　merely　determining　the　TOF　such　as　the　direct　method　and　the　deconvolution　method　might　be　compromised.　Here　we　have　proposed　the　sparse　representation　(SR)　method　to　quantitatively　characterize　the　layer　thickness　by　reconstructing　the　impulse　response　from　complex　THz　echo　signals.　To　balance　the　accuracy　and　the　computational　efficiency,　we　have　proposed　a　combinational　search　method　for　selecting　the　optimal　regularization　parameter　and　constructed　a　convolution　dictionary　based　on　the　structural　prior　of　THz　reference　echo　during　the　sparse　decomposition　process.　Both　numerical　and　experimental　analysis　are　performed　to　validate　the　robustness　of　SR　method　on　the　THz　echo　localization　compared　with　those　conventional　methods.　It　can　be　expected　that　SR　will　provide　a　novel　approach　to　the　application　of　precise　localization　and　quantification　of　defects　in　THz　based　nondestructive　techniques.　©　2021　Elsevier　Ltd