Considering the prior knowledge of SAR image in spatial domain and the property of coefficients in wavelet domain, this paper presents a novel algorithm of SAR image despeckling: constructing an adaptive window and finding a uniform region for every pixel of SAR image by using Local Polynomial Approximation-Intersection of Confidence Intervals (LPA-ICI), implementing hard-threshold shrinkage with fast shape adaptive discrete wavelet transform proposed in this paper. At last, many despeckled samples are fused into a final despeckled SAR image according to the sparsity of regions, which is presented in this paper. Experiments show that the algorithm proposed in this paper has advanced despeckled performance. Especially, reconstructed image is absent from unpleasant ringing artifacts, and efficiently reserves point targets of original SAR image.