We propose a novel total variation (TV) regularization model for synthetic aperture radar (SAR) image despeckling. A method combined with second-order and fourth-order TV sparse constraints is applied to reconstruct and despeckle SAR image. Experiments have been carried out in echo domain using GF-3 spaceborne SAR raw data. We introduce the target-to-clutter ratio (TCR) to quantitatively assess the SAR image quality and the effectiveness of target detection and multiplicative noise suppression. Experimental results show that the proposed second-order and fourth-order TV method can further effectively suppress SAR image speckles without compromising the details of image features according to both subjective visual assessment of image quality and objective evaluation using TCR.