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It is well known that at low-bit-rate block discrete cosine transform compressed image exhibits visually annoying blocking and ringing artifacts. In this paper, we propose a noniterative, wavelet-based deblocking algorithm to reduce both types of artifacts. The algorithm exploits the fact that block discontinuities are constrained by the dc quantization interval of the quantization table, as well as the behavior of wavelet modulus maxima evolution across wavelet scales to derive appropriate threshold maps at different wavelet scales. Since ringing artifacts occur near strong edges, which can be located either along block boundaries or within blocks, suppression of block discontinuities does not always reduce ringing artifacts. By exploiting the behavior of ringing artifacts in the wavelet domain, we propose a simple yet effective method for the suppression of such artifacts. The proposed algorithm can suppress both block discontinuities and ringing artifacts effectively while preserving true edges and textural information. Simulation results and extensive comparative study with both iterative and noniterative methods reported in the literature have shown the effectiveness of our algorithm.