A signal reconstruction algorithm based on the compressed sensing (CS) theory with dual-uniform sampling point (DUSP) distribution is developed and applied to identify the azimuthal mode of axial compressor. A regular failure signal pattern is found, and the corresponding explanation is presented with validation. Azimuthal mode analysis is applied to both numerical and experimental pressure fluctuation signals of rotating instability (RI) in the axial compressor tip region. For numerical calculations, the signal in the azimuthal mode domain is reconstructed by the CS with random measurement points and DUSP, respectively. The success rates and reconstruction errors are discussed in detail. It is shown that the azimuthal mode reconstruction method based on CS combined with DUSP is capable of identifying the complex flow modes in the tip region of the axial compressor. For the experimental results, high azimuthal mode orders are reconstructed based on dynamic pressure signals measured by DUSP. Azimuthal mode analysis efficiency is thereby significantly improved. The time-resolved characteristics of the RI are discussed. Moreover, a robustness analysis is conducted, demonstrating the ability of the CS-based method with DUSP to address sensor failure problems.