This paper proposes an inverse method to characterize wave and energy propagation in curved structures, addressing the challenges of accurately obtaining dispersion curves, wavenumber space, and damping loss factors caused by their complex dynamics. The proposed method, Generalized Algebraic K-Space Identification (GAKSI) technique, is developed within the algebraic identification framework, enables the extraction of complex wavenumbers of multidimensional signals from full-field measured maps for the first time. By introducing iterated integrals and multivariate Laplace transform, the method can effectively filter signal noise, enhancing the accuracy of extracted wave propagation parameters. In this paper, the proposed method is applied to isotropic open shells with different geometric parameters and a real honeycomb cylindrical shell. Extracted results are compared with those from the reference methods. An in-depth analysis compares the characterization of shells and plates under varying signal noise levels. The findings demonstrate that the proposed method achieves high precision even under noisy conditions: the relative error for the extracted wavenumber converges to around 2.5% when the signal-to-noise ratio (SNR) exceeds 5, while the relative error for the extracted damping loss factor converges to approximately 5.5% when the SNR exceeds 10. Furthermore, the observations reveal that curvature-induced bending-membrane coupling enhances the damping properties, with this effect becoming more pronounced as the wave propagation direction transitions from the axial to the circumferential direction. These findings validate the capability of proposed method to characterize dispersion and damping properties in curved structures, offering promising potential for further applications in structural analysis, such as structural optimization and design.