Combined with the characteristics of synthetic aperture radar（ SAR）

a compressed-sensing SAR image reconstruction method based on modified smoothed L0（ MSL0） is proposed. The method approximates the discrete L0 norm with a larger approximation hyperbolic function of"steepness"

and transforms the L0 norm minimization problem in the compressed sensing SAR image reconstruction into the minimum optimization problem of the smooth function. Secondly

for the smoothed L0（ SL0） norm algorithm

"Saw-tooth phenomenon"occur caused by using steepest descent method leads to the disadvantage of increasing the SAR image reconstruction time and the low resolution of the reconstructed SAR image

and introducing a hybrid optimization algorithm. The algorithm combines the advantages of the steepest descent method and the quasi-Newton method to improve the speed and precision of SAR image reconstruction. Experiments show that under the same external conditions

the performance of SAR image reconstruction methods proposed in this paper is greatly improved.