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A compression method for image data with very high resolution, and an evolvable hardware chip implementing the process quickly are proposed. The current international standard for bi-level image coding, JBIG2, is modified by the proposed method to achieve high compression ratios, where compression parameters are optimised by search methods (primarily a genetic algorithm that has been extended and specialised for this problem). The results of computer simulations show a 23% improvement in compression ratios with the proposed method compared to JBIG2, and demonstrate that the optimisation process can be completed very quickly, even with software execution. The experiment shows that when the method is implemented by hardware with an evolvable hardware chip, the processing is dramatically faster than execution with software. Activities concerning ISO standardisation to adopt part of the technology used in this method to the JBIG2 standard are also described.