An integer hierarchy lapped biorthogonal transform via lifting steps and application in image coding

By using integer discrete cosine transform (IntDCT) based on lifting steps, we in this paper introduce an integer hierarchy lapped biorthogonal transform via lifting steps called the IntHLBT. When all elements with floating-point of each lifting matrix in the IntHLBT is approximated by the binary fractions, the IntHLBT is implemented by a series of dyadic lining steps, and provides very fast, efficient in-place computation of the transform coefficients, so it can express image information as lossless. As applications of the novel IntHLBT to lossy image compression, simulation results demonstrate that the IntHLBT has significantly less blocking artifacts, higher peak signal-to-noise ratio (PSNR), and better visual quality than the DCT Moreover, the IntHLBT´s coding performance is approximately the same as that of the much more complex Cohen-Daubechies-Feauveau (CDF) 9/7 biorthogonal wavelet with floating-point coefficients, and in some cases, even surpasses that of CDF 9/7 biorthogonal wavelet.