The segmented planar imaging detectors have attracted intensive attention because of its superior imaging performance and structural compactness. The structure of radial SPIDER is investigated and the imaging progress is mathematically analyzed according to the Van Cittert-Zernike theorem. Due to the sparse sampling density in the frequency domain resulted from restriction of the structure, the imaging quality of SPIDER is unsatisfactory. In this paper, a reconstruction algorithm based on the compressed sensing theory is proposed to reconstruct the sparse signal from far fewer sampling density than the Nyquist–Shannon sampling criterion. The objective function, measurement matrix and sparse matrix are discussed according to the physical mechanism of SPIDER. The TV/L1 minimization and alternating direction multiplier method (ADMM) are used to obtain high-resolution images. Simulation results of image reconstruction demonstrate that the imaging resolution is improved remarkably than the original image.