O. Pogrebnyak, P.M. Ramírez, and J.U. Sossa Azuela (Mexico)
Wavelets, Non-linear wavelet transform, Image compression, Noise suppression
Novel algorithms of image DWT transform with non separable 2D kernels are presented. The algorithms operate on byte represented images and perform image transformation using the well-known lifting scheme. The proposed algorithms use the modified “checkerboard” subsampling scheme for non separable 2D wavelet kernels drastically reducing geometrical distortions. The problem of data extension near the image borders is resolved by computing the Haar wavelet in the neighborhood of the borders. The first algorithm is a linear DWT based on the Cohenen-Daubechies-Feauveau wavelet of the second order factorized for the non-separable 2D lifting. The second algorithm is non-linear, and uses the 2D median calculation at the prediction stage providing the adaptation in the vicinity of edges. The presented algorithms do not possess perfect restoration of the processed data because of the normalization and rounding that are introduced at the each level of decomposition/restoration to perform operations with byte represented data. However, the visual and quantitative quality of the restored images is high enough allowing the use of the designed algorithm in image compression and noise suppression applications. In the paper it is shown that the non linear median DWT algorithm outperforms the linear one in lossy compression providing better visual quality of the restored images.
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