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Set partition coding (SPC) has shown tremendous success in image compression. Despite its popularity, the lack of error resilience remains a significant challenge to the transmission of images in error-prone environments. In this paper, we propose a novel data representation called the progressive significance map (prog-sig-map) for error-resilient SPC. It structures the significance map (sig-map) into two parts: a high-level summation sig-map and a low-level complementary sig-map (comp-sig-map). Such a structured representation of the sig-map allows us to improve its error-resilient property at the price of only a slight sacrifice in compression efficiency. For example, we have found that a fixed-length coding of the comp-sig-map in the prog-sig-map renders 64% of the coded bitstream insensitive to bit errors, compared with 40% with that of the conventional sig-map. Simulation results have shown that the prog-sig-map can achieve highly competitive rate-distortion performance for binary symmetric channels while maintaining low computational complexity. Moreover, we note that prog-sig-map is complementary to existing independent packetization and channel-coding-based error-resilient approaches and readily lends itself to other source coding applications such as distributed video coding.