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We propose a method for removal of compression artifacts that exploits the statistical properties of image patches in local shifted windows. As will be shown, the compression artifacts are efficiently captured by the principal components corresponding to the small singular values of the local region. Both of the blocking and ringing artifacts are effectively eliminated by suppressing these principal components. We further show that the proposed method can be reformulated into a regularized least squares problem. Two regularization techniques: truncated SVD and Tikhonov regularization are introduced. The regularization parameters for the proposed least squares model are derived using Bayesian analysis. The experimental results indicate that the proposed algorithm outperforms many existing methods on both objective and subjective measurements.