Summary: The mathematical formulation used in tomography has been successfully applied to time-frequency analysis, which represents an important “imaging modality” of the structure of signals. Based on the interrelation between computer tomography (CT) and time-frequency analysis, new methods have been developed for the latter. In this paper, an original method for constructing the time-frequency representation of signals from the squared magnitudes of their fractional Fourier transforms is presented. The method uses $α$-norm minimization with $α\to 1$ which is motivated by Rényi entropy maximization. An iterative optimization method with adaptive estimation of the convergence parameter is elaborated. The proposed method exhibits advantages in the suppression of interference terms for signals with simple time-frequency configurations.