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This paper proposes joint-probability-based adaptive Golomb coding (JPBAGC) to improve the performances of the Golomb family of codes, including Golomb coding (GC), Golomb-Rice coding (GRC), exp-Golomb coding (EGC), and hybrid Golomb coding (HGC), for image compression. The Golomb family of codes is ideally suited to the processing of data with geometric distribution. Since it does not require a coding table, it has higher coding efficiency than Huffman coding. In this paper, we find that there are many situations in which the probability distribution of data is not only geometric, but also depends on the probability distribution of the other data. Accordingly, we used the joint probability of generalizing the Golomb family of codes and exploiting the dependence between neighboring image data. The proposed JPBAGC improves the efficiency of many image and video compression standards, such as the joint photographic experts group (JPEG) compression scheme and the H.264-intra JPEG-based image coding system. Simulation results demonstrate the superior coding efficiency of the proposed scheme over those of Huffman coding, GC, GRC, EGC, and HGC.