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In the traditional approach of block transform image coding, a large number of bits are allocated to the DC coefficients. A technique called DC coefficient restoration (DCCR) has been proposed to further improve the compression ability of block transform image coding by not transmitting the DC coefficients but estimating them from the transmitted AC coefficients. Images thus generated, however, have inherent errors that degrade the image visual quality. In the paper, a global estimation DCCR scheme is proposed that can eliminate the inherent errors. The scheme estimates all the DC coefficients of the blocks simultaneously by minimising the sum of the energy of all the edge difference vectors of the image. The performance of the global estimation DCCR is evaluated using a mathematical model and experiments. Fast algorithms are also developed for efficient implementation of the proposed scheme.