Invertible integer DCT applied on progressive until lossless image compression

This paper completes the construction of FFT (fast Fourier transform) that map integers to integers by using lifting scheme and butterfly-style construction. Through building integer FFT which keeps conjugate symmetry for real signal, and expressing DCT by FFT, invertible integer DCT can be easily gotten, which makes lossless image compression possible. At last, we combine integer DCT with EZW zerotree and STQM arithmetic coding together. Experimental results show this method is quite efficient for progressive until lossless image compression.