Invertible integer FFT applied on lossless image compression

Integer transform is crucial for lossless compression. Integer wavelet transform's promising exploration attributes to lifting scheme. This paper employs lifting scheme to FFT's butterfly, and presents the construction of invertible FFT (fast Fourier transform) that maps integers to integers, which leads to the building of invertible integer DCT. On the other hand, for color image, an integer transform between color spaces based on lifting scheme is built. Experimental results using invertible integer DCT for lossless and lossy color image compression are given and show that this transform is fast and efficient.