An apparatus has a one-dimensional DCT transformer for applying the one-dimensional orthogonal transforms to n inputs and outputting n coefficients, a transposition converter for transposing n.times.n coefficients output from the one-dimensional DCT transformer and outputting every n outputs, and a multiplexer for selecting one output of the n outputs from the transposition converter or one output of the n outputs from the one-dimensional DCT transformer. The apparatus further includes a selector for selecting data as a combination of one output selected by the multiplexer and remaining (n-1) outputs, which are not input to the multiplexer, of the n outputs from the transposition converter, or the input image data, and supplying the selected data as n data to the one-dimensional DCT transformer.