New family of lapped biorthogonal transform via lifting steps

By scaling all discrete cosine transform (DCT) intermediate output coefficients of the lapped transform and employing the type-II and type-IV DCT based on lifting steps, a new family of lapped biorthogonal transform is introduced, called the IntLBT. When all the elements with a floating point of each lifting matrix in the IntLBT are approximated by binary fractions, the IntLBT is implemented by a series of dyadic lifting steps and provides very fast, efficient in-place computation of the transform coefficients, and all internal nodes have finite precision. When each lifting step in the IntLBT is implemented using the same nonlinear operations as those used in the well known integer-to-integer wavelet transform, the IntLBT maps integers to integers, so it can express lossless image information. As an application of the novel IntLBT to lossy image compression, simulation results demonstrate that the IntLBT has significantly less blocking artefacts, higher peak signal-to-noise ratio, and better visual quality than the DCT. More importantly, the IntLBT's coding performance is approximately the same as that of the much more complex Cohen-Daubechies-Feauveau (CDF) 9/7-tap biorthogonal wavelet with floating-point coefficients, and in some cases even surpasses that of the CDF 9/7-tap biorthogonal wavelet.