关键词: 图像压缩, 整数变换, 非连续正交U系统, 吉布斯现象, 快速计算

Abstract:

The integer transform methods are widely adopted in international image and video coding standards due to their fast computation strategies. Existing integer transform methods are generated from continuous orthogonal systems, which not only makes it difficult to obtain precise integer forms of original transforms, but also cannot overcome the Gibbs phenomenon in discontinuous signal representation, reducing the quality of reconstructed images. Thus, a new integer transform and its image compression method based on discontinuous U-system are proposed. Firstly, the piecewise integration and the Gram-Schmidt process are used to calculate the two-dimensional orthogonal matrix of the U-system, and the scaling factors of row vectors are extracted to obtain the integer matrix. Secondly, the reversible integer U transform is established, and the integer matrix is applied to concentrate the energy of images into a small amount of data sets, while merging scaling factors with quantization to reduce computational burden. Then, the fast integer U transform is achieved by using matrix decomposition and sparse matrices. Finally, the integer U transform module and inverse transform module are designed to alleviate the pressure of image storage and transmission. Experimental results show that the proposed method can reduce truncation errors of reversible image transform compared with related algorithms; the new method obtains higher compressed image quality in image and video compression experiments, and the fast transform algorithm effectively saves computational time.

Key words: image compression, integer transform, discontinuous orthogonal U-system, Gibbs phenomenon, fast computation