Construction Of True Bidimensional Wavelets On Lifting Scheme And Application In Image Coding

This paper focuses on the construction of true bidimensional wavelets by lifting scheme and the relevant image coding. We research the nonseparable bidimensional interpolator designed by different standards, carry out the true bidimensional wavelet decomposition and improve the SPIHT coding in order to adapt to the characteristic of true bidimensional wavelet decomposition. It is proved by experiments that the subjective and objective quality of binary tree SPIHT on true bidimensional wavelet decomposition is better than famous 9/7 wavelet under the condition of low bits compression.This paper proposes a novel interpolator that is the All Phase Inverse Discrete Cosine Sequency Filter (APIDCSF). Based on the theory of the All Phase, the APIDCSF considers the surrounding samples'influence on the center one throughly, and takes the average of IDCT orthogonal filtering of surrounding sampling blocks which include the center sample as its orthogonal transformed value. Coefficient distribution of the APIDCSF is similar to that of circular quincunx Neville filter and its interpolating performance outperforms the Neville filters with high orders vanishing moments (VMs).The aim of bidimensional interpolating is to diminish the error between the true value and the estimated one. For this objection, we propose a kind of optimal interpolator in the senes of the minimizing mean square error (MSE), which using the image nonseparable autocorrelation function model and characteristic of circular quincunx interpolator's coefficient distribution. The experiments testified that the interpolating characteristic of APIDCSF is similar to the optimal interpolator. A quasi-vanishing moment curve is proposed here. The interpolating capability of filter with higher order VMs is better than the one with lower order VMs, and the interpolating capability of filter with bigger support is better than the one with smaller support. Under the same support, the quasi-VMs can check the semblance between filters with higher order VMs and the ones with lower order VMs.On lifting scheme, this paper constructs the true bidimensional FB, which takes the APIDCSF and optimal circular interpolator as predict and update operators. Although the two true bidimensional wavelet FBs have two order VMs, we compare them with the Neville FBs with the same support but high order VMs. Theexperiments show that the energy of subband decomposed by the two kind of true bidimensional wavelet FBs is similar to that of the Neville wavelet FB with the same support but high order VMs.Because the decomposition of true bidimensional wavelet is different from the separable bidimensional wavelet, this paper proposes two kind of binary tree coding by improved SPIHT coding: the space orientation binary tree SPIHT and the knot binary tree SPIHT. In low bit compression, the PSNR of image coding by two kind binary tree SPIHT is higher than the quadtree SPIHT with 9/7 wavelet decomposition, especially the PSNR obtained by the knot binary tree SPIHT is higher than the quadtree SPIHT about 1 dB. Experiment results show that binary tree SPIHT suits to true bidimensional wavelet decomposition and it is testified that in true bidimensional wavelet decomposition, the compression effect is comparable between image decomposed by wavelet FB with low order VMs but good interpolating characteristic and that with higher order VMs.