Speckle noise can reduce the image quality of synthetic aperture radar (SAR) and complicate image interpretation. This study proposes a novel three-step approach based on the conventional probabilistic patch-based (PPB) algorithm to minimize the impact of bright structures on speckle suppression. The first step improves the calculation accuracy of the weight by pre-processing speckle noise with a linear minimum mean-square error filter and reassessing similarity between pixels. In the second step, an iterative method is developed to avoid interfering with bright structures and acquires a more accurate homogeneous factor by adaptively changing the size of the search window. In the final step, the spreading and blurring of bright structures is corrected using a modified bias-reduction technique. Experimental results demonstrate the proposed algorithm has improved performance for both speckle suppression and preservation of edges and textures, evaluated by indicators including the equivalent number of looks, the edge preservation index, the mean, and standard deviation of ratio images.