Azimuthal mode analysis (AMA) is one of the most commonly used approaches for comprehending the characteristics of the noise emitted from the aero-engine fans. This paper proposed a new azimuthal mode detection method based on compressive sensing, which breaks through the limitations of the Shannon-Nyquist sampling theorem and extends the range of mode detection. A $\ell_{0}$ -norm regularized AMA method is proposed to reconstruct the spectrum of the tonal modes of aero-engine fans. Notably, the orthogonal matching pursuit (OMP) algorithm is implemented to effectively ameliorate the solution of the $\ell_{0}$ -norm regularized problem. The feasibility of the proposed approach is verified by a series of simulations, of which the configurations are consistent with a practical case. Meanwhile, the performance of the $\ell_{1}$ -norm regularized AMA method is compared with the proposed approach. The simulation results indicated that the $\ell_{0}$ -norm regularized approach enhanced the sparsity of the estimations of the tonal noise mode spectrum. The stability and the robustness of the reconstruction results are notably improved, which leads to a higher accuracy of the amplitudes of the tonal acoustic modes and a noticeable reduction of the number of the microphones required by AMA.