By considering the prior knowledge of SAR image in spatial domain and the property of coefficients in wavelet domain， a novel algorithm of SAR image despeckling was presented. An adaptive window was constructed and a uniform region for every pixel of SAR image was found by using local polynomial approximation-intersection of confidence intervals (LPA-ICI). Hard-threshold shrinkage despeckling was implemented with fast shape adaptive discrete wavelet transform proposed in this paper. At last， many despeckled samples were fused into a final despeckled SAR image according to the sparsity of regions. Experiments show that the algorithm proposed here has advanced despecking performance. Especially， reconstructed image has no unpleasant ringing artifacts， and it efficiently reserves point targets of original SAR image.