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A lossless compression of an error-diffused image by lossless coding of entropy-minimized multi-level image, which can produce given halftone image at the receiver side, is studied. Through the study, block-type error diffusion is introduced to consider the two-dimensional entropy, and both of entropy-based prioritisation method and prediction-error-based prioritisation method in inverse halftoning procedure are proposed and compared. The result shows that the restored image by proposed methods has about 40% less entropy than that of the original multi-level image, but 50-70% larger than that of halftone image. However through the simulation of pseudo high resolution images, it was expected that the proposed method could even show less entropy than that of the bi-level image in higher resolution cases.