## 1 Introduction
[22] used piezoelectric wafer active sensors (PWASs) adhered to the surface of structures as units to drive and sense ultrasonic guided waves, proposing a frequency tuning method to select the specific \(S_{0}\) mode ultrasonic guided wave with relatively weak dispersion characteristics. They employed a time-domain DAS algorithm under the far-field plane wave approximation to map the amplitude information corresponding to the transit time into space, thereby achieving imaging detection of pre-existing crack damage in aluminum plate structures. [PERSON] et al. [23] further extended the time-domain DAS algorithm to the near field, constructing an embedded ultrasonic structural radar system based on a guided wave phased array method [24]. They analyzed the effects of different array parameters, such as the number of elements, spacing, and array configuration, on the all-around guided wave beam driving. [PERSON] et al. [25] investigated the capabilities of piezoelectric array transducers in driving wave beams in different directions using a similar approach. The time-domain DAS selected weakly dispersive modes (such as the \(S_{0}\) mode in the low-frequency range) to mitigate the effects of guided wave dispersion, which somewhat limited the frequency range of guided waves to comprehensively capture all information regarding damages. [PERSON] et al. [15] introduced the Sign Coherence Factor-Total Focusing Method (SCF-TFM) to address resolution degradation caused by Lamb wave dispersion. However, the method still lacks precise dispersion compensation mechanisms that could more effectively improve the accuracy of defect localization and sizing. Addressing the dispersion issue of guided waves, researchers have further developed a frequency-domain method that implements delay-and-sum in the frequency domain [26; 27], capable of incorporating wave equations that include dispersion relations into the calculations, thereby obtaining precise damage scattering sources. To consider the impact of the dispersion characteristics of multimodal guided waves, [PERSON] [27] proposed a method for omnidirectional probing in large-area plate structures based on the frequency-domain DAS algorithm under the condition that the dispersion characteristics are known and compared the imaging effects of circular and annular arrays. [PERSON] and [PERSON] [26] further advanced the frequency-domain DAS method for damage detection in composite plate structures, achieving accurate imaging detection of pre-existing damage in carbon fiber-reinforced composite plates while considering the angular correction between phase velocity and group velocity and the material anisotropy. [PERSON] et al. [14] proposed a full-focus imaging algorithm combining frequency-domain backpropagation and phase/waveform coherence analysis (SCF-WCF), which significantly improves defect detection accuracy and robustness in noisy environments. In summary, the frequency-domain ultrasonic guided wave DAS imaging method allows for the separate calculation of time or phase delays for each frequency component, achieving higher imaging localization accuracy and multi-damage imaging resolution under the premise of known dispersion characteristics. However, some researchers point out [28] the theoretical framework for guided wave scattering in the aforementioned methods still falls within the Born approximation category, making it difficult for the imaging resolution to surpass the diffraction limit. In research related to the Time Reversal Method (TRM) and its iterative approaches aimed at achieving adaptive focusing of the wave field at scattering sources, researchers often use the Scattering Matrix to describe the multi-path mapping relationship between multiple input and output signals [29]. The system's Time Reversal Operators (TROs) are then obtained through the Scattering Matrix, thereby inverting the entire process of guided wave propagation from excitation to scattering to sensing.