This article presents a quantitative Lamb wave detection method for delamination characterization in composite laminates using local wavenumber features. In contrast to the conventional Fourier transform-based methods, the improved sparse reconstruction method is efficient and able to evaluate the spatial wavenumbers of Lamb waves with limited measurements. To improve the feasibility of the sparse reconstruction method, the analytical solution of the local wavenumbers to the compressed sensing (CS) formulation with considering structural discontinuity is firstly investigated. The estimated wavenumber values for the spatial window located on healthy and damaged regions simultaneously are governed by a nonlinear optimization function. Benefiting from revealing the evolution of local wavenumber slopes, a delamination characterization method is proposed to accurately determine the damage location and depth by wavenumber banalization. Subsequently, the performance of the proposed method on local wavenumber estimation and damage quantification is verified by the simulation data. The parameters are discussed in order to improve the algorithm stability. Finally, the experimental investigation was conducted on a quasi-isotropic carbon fiber reinforced polymer (CFRP) laminate with an induced delamination. Lamb wave was generated and scanned by the Nd:YAG laser spot with spatial intervals of 2 mm. The results verify the sparse reconstruction method for delamination characterization, which shows value of reducing labor cost and testing time.