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In order to reduce the blocking artifact in the Joint Photographic Experts Group (JPEG)-compressed images, a new noniterative postprocessing algorithm is proposed. The algorithm consists of a two-step operation: low-pass filtering and then predicting. Predicting the original image from the low-pass filtered image is performed by using the predictors, which are constructed based on a broken line regression model. The constructed predictor is a generalized version of the projector onto the quantization constraint set , , or the narrow quantization constraint set . We employed different predictors depending on the frequency components in the discrete cosine transform (DCT) domain since each component has different statistical properties. Further, by using a simple classifier, we adaptively applied the predictors depending on the local variance of the DCT block. This adaptation enables an appropriate blurring depending on the smooth or detail region, and shows improved performance in terms of the average distortion and the perceptual view. For the major-edge DCT blocks, which usually suffer from the ringing artifact, the quality of fit to the regression model is usually not good. By making a modification of the regression model for such DCT blocks, we can also obtain a good perceptual view. The proposed algorithm does not employ any sophisticated edge-oriented classifiers and nonlinear filters. Compared to the previously proposed algorithms, the proposed algorithm provides comparable or better results with less computational complexity.