Coherent transition radiation (CTR) spectroscopy has emerged as a highly productive technique for measuring bunch length and reconstructing longitudinal bunch profiles. However, conventional Michelson interferometry is limited to the amplitude measurement of terahertz radiation spectra, rendering it incapable of directly reconstructing the bunch profile owing to the absence of phase information. Currently, the predominant reconstruction methods encompass the Kramers-Kronig (K-K) phase analysis and algebraic iterative reconstruction algorithms. These two algorithms were employed to validate both Gaussian distribution and Gaussian distribution with tail models, respectively. The outcomes obtained from the K-K algorithm exhibit notable uncertainty, whereas the iterative algorithm showcased superior performance in resolving reconstruction ambiguities and mitigating noise interference. Within the framework of the Lanzhou High Energy Electronic Imaging Platform, a specialized Michelson interferometer was meticulously engineered for the precise measurement of CTR interference spectra. Subsequent to two distinct measurements, the acquired data was subjected to reconstruction and comprehensive analysis employing the aforementioned algorithms. As a result, detailed longitudinal beam cluster reconstructions for the electron beam were successfully obtained. These findings constitute a reference for subsequent beam diagnosis and feedback mechanisms within the High Energy Electron Beam Imaging Platform.