Synthetic aperture radio telescopes are important in the radio astronomy field. However, the inverse imaging process of these telescopes is an ill-posed inverse problem. Although the compressed sensing technology represented by the sparsity averaging reweighted analysis (SARA) algorithm has been successfully applied to the imaging of the synthetic aperture radio telescope, large reconstruction errors remain in the traditional SARA algorithm due to its difficulty in selecting soft threshold parameters. Therefore, an improved SARA algorithm is proposed. This algorithm uses an improved projected fast iterative soft thresholding algorithm to solve the minimization model, adaptively updates soft threshold parameters by fully utilizing data fidelity and regularization terms, and adopts restarting and adaptive strategies to accelerate convergence, thereby improving the overall accuracy and speed of inversion imaging. The simulation results demonstrate that compared with the traditional compressed sensing algorithm, the improved SARA algorithm can effectively reduce reconstruction error and increase calculation speed, thus proving its effectiveness.