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The block-based discrete cosine transform (BDCT) is often used in image and video coding. It may introduce block artifacts at low data rates that manifest themselves as an annoying discontinuity between adjacent blocks. In this paper, we address this problem by investigating a transform-domain Markov random field (TD-MRF) model. Based on this model, two block artifact reduction postprocessing methods are presented. The first method, referred to as TD-MRF, provides an efficient progressive transform-domain solution. Our experimental results show that TD-MRF can reduce up to 90% of the computational complexity compared with spatial-domain MRF (SD-MRF) methods while still achieving comparable visual quality improvements. We then discuss a hybrid framework, referred to as TSD-MRF, that exploits the advantages of both TD-MRF and SD-MRF. The experimental results confirm that TSD-MRF can improve visual quality both objectively and subjectively over SD-MRF methods.