In a method for compressing an image, a number of non-zero AC coefficients for a component transform and the locations of the non-zero AC coefficients in a transform block are determined. One of a plurality of coding modes is selected in response to the number of non-zero AC coefficients and the locations of the non-zero AC coefficients satisfying predetermined criteria, where the plurality of coding modes comprise different bit allocations from each other. In addition, the locations and values of the non-zero AC coefficients and a DC coefficient for the component transform are coded according to the selected coding mode, to thereby compress the image.