A Study Of Biorthogonal Wavelet Transforms Based On Essentially Non-Oscillatory In Image Compression

Only using coarse scale wavelet coefficients to reconstruct, standard wavelet transforms cannot possess excellent properties for general images which typically are piecewise continuous functions connected by large jumps. Many problems arise near these jumps, caused primarily by the well-known Gibbs'phenomenon. To remove the effects of Gibbs'phenomenon completely, we bring forward an ENO-Biorthogonal wavelet transforms arithmetic combining with ENO method. In this arithmetic, we needn't modify the Biorthogonal wavelet transforms and the filter coefficients. In forward algorithm, we according to the high level coefficients to locate the jumps and modify the coarser level coefficients, which relate with the jumps. In inverse transforms algorithm, according to the locations to modify the datum, which relate with the jumps. We can reconstruct the image well by using this algorithm, and avoid the Gibbs' phenomenon completely.The ENO-Biorthogonal wavelet transforms are fit for compressing the images which contain a great lot jumps, and having good ratio of compression. We use period extension or symmetry extension in image processing. Our arithmetic has perfect properties that validated by numeric experiments in image compression.