In many image coding methods, the discrete cosine transform (DCT) is used. When the compression ratio is increased, blocking artifacts are generated in the reconstructed image due to quantization error. To resolve this problem, a method is proposed to adaptively change the suppression process of distortion depending on the block. In this method, each block is classified into (1) the flat part where the pel values change monotonically by the value of the received DCT coefficient and (2) the dynamic part. In the block in the flat part, the DCT coefficients are estimated within the quantization width by the quadratic programming method, and the block is regenerated by replacing the received coefficients. The continuity at the block boundary and the boundary pel values after smoothing are used as the objective function. Higher‐order DCT coefficients can be estimated successively. In the region where the variation of the pel values is substantial, human visual sensitivity is not sufficient for the distortion. Therefore, the block boundary is smoothed with a low‐pass filter (LPF) in the block in the variable part. This method is used for processing of several images. It is demonstrated that the SNR is better than those in the JPEG reconstruction method, ac coefficient prediction method, and the LPF method. Overall, a high‐quality reconstructed image is obtained with the blocking artifacts are suppressed. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(4): 50–59, 2001