Abstract: A method of generating an output array of image spatial frequency coefficients from input arrays of image spatial frequency coefficients overlapped by the required array, the spatial frequency coefficients being transformable to image pixel values by a predetermined spatial frequency transformation, comprises the steps of: matrix-multiplying each input array by one or more respective matrices having coefficients derivable by applying the inverse of the predetermined spatial frequency transformation to respective translation matrices which, if matrix-multiplied by that input array, would provide a translation of the overlapped portion of that input array to an overlapping position in the output array; and matrix-adding the respective matrix products generated from each overlapped input array.