1. A method of resizing an image using a resizing ratio, comprising: receiving a DCT (Discrete Cosine Transform) coefficient matrix Y×X of an input image; calculating a transformation matrix for transforming the DCT coefficient matrix Y×X of the input image using an integer aspect ratio closest to the target resizing ratio; performing a coarse resizing on the DCT coefficient matrix Y×X of the input image in a DCT domain using the transformation matrix; obtaining a spatial image by performing an IDCT (Inverse Discrete Cosine transform) on the coarse-resized image; and forming an output image having a coefficient matrix y×x by performing a fine resizing on the spatial image in a spatial domain, wherein the calculating of the transformation matrix includes: calculating N′ that satisfies Y:y=N:N′ and calculating M′ that satisfies X:x=M:M′, where N and M are the number of vertical direction coefficients and the number of horizontal direction coefficients in a coefficient matrix of an DCT filter; selecting integers N″ and M″ closest to the calculated decimal fractions N′ and M′; and calculating an N″×N″ transformation matrix and an M″×M″transformation matrix using N″ and M″, Y denotes the number of pixels in a vertical direction of the input image, X demotes the number of pixels in a horizontal direction of the input image, y denotes the number of pixels in a vertical direction of the output image, an x denotes the number of pixel in a horizontal direction of the output image, and the performing of the coarse resizing includes calculating an N″×M″ transformation matrix of the input image using the N″×N″ transformation matrix and the M″×M″ transformation matrix.