华南理工大学学报(自然科学版) ›› 2024, Vol. 52 ›› Issue (10): 124-134.doi: 10.12141/j.issn.1000-565X.230784

所属专题: 2024年图像处理

• 图像处理 • 上一篇    下一篇

基于整数U变换的图像压缩方法

袁茜茜1,2(), 蔡占川3, 石武祯1(), 尹文楠1   

  1. 1.深圳大学 电子与信息工程学院/广东省数字创意技术工程实验室,广东 深圳 518060
    2.广东工业大学 计算机学院,广东 广州 510006
    3.澳门科技大学 创新工程学院,澳门 999078
  • 收稿日期:2023-12-24 出版日期:2024-10-25 发布日期:2024-03-22
  • 通信作者: 石武祯 E-mail:xxyuan@gdut.edu.cn;wzhshi@szu.edu.cn
  • 作者简介:袁茜茜(1992—),女,博士,讲师,主要从事计算机图形图像处理研究。E-mail: xxyuan@gdut.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(62101346);广东省重点领域研发计划项目(2022B0101010001);广东省基础与应用基础研究基金资助项目(2021A1515011702)

Image Compression Method Based on the Integer U Transform Algorithm

YUAN Xixi1,2(), CAI Zhanchuan3, SHI Wuzhen1(), YIN Wennan1   

  1. 1.College of Electronics and Information Engineering/ Guangdong Provincal Engineering Laboratory for Digital Creative Technology,Shenzhen University,Shenzhen 518060,Guangdong,China
    2.School of Computer Science and Technology,Guangdong University of Technology,Guangzhou 510006,Guangdong,China
    3.Faculty of Innovation Engineering,Macau University of Science and Technology,Macau 999078,China
  • Received:2023-12-24 Online:2024-10-25 Published:2024-03-22
  • Contact: SHI Wuzhen E-mail:xxyuan@gdut.edu.cn;wzhshi@szu.edu.cn
  • Supported by:
    the National Natural Science Foundation of China(62101346);the Key-Area R & D Program of Guangdong Province(2022B0101010001);the Basic and Applied Basic Research Foundation of Guangdong Province(2021A1515011702)

摘要:

整数变换方法因其较快的计算速度被国际图像和视频编码标准广泛采纳。现有基于连续正交函数系的整数变换方法不仅难以获得原始变换的准确整数形式,而且无法克服在非连续信号表达时出现的吉布斯震荡现象,降低了重构图像质量。为此,文中提出了基于非连续正交U系统的整数变换算法及其图像压缩方法。首先,采用分段积分法和施密特正交化法计算出U系统的2维正交变换矩阵,提取行向量的缩放因子得到整数矩阵;接着,建立整数U矩阵的可逆正交变换方法,使用整数矩阵将离散图像信息的能量集中到少量数据集,同时将缩放因子与量化步骤合并以减轻计算负担;然后,采用矩阵分解法将整数U矩阵分解为稀疏矩阵的乘积,从而实现图像变换的快速计算;最后,设计基于整数U变换模块和逆变换模块的图像压缩方法,用于减轻图像存储和传输压力。实验结果表明:文中方法与其他相关方法相比,可以降低图像可逆变换的截断误差;在图像和视频压缩实验中,在相同的压缩率下文中方法获得的压缩图像质量更高,而且快速变换方法可以有效地节省运算时间。

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 because of its fast calculation speed. The existing integer transform methods based on the continuous orthogonal function system not only struggle to obtain the exact integer form of the original transform, but also fails to overcome the Gibbs oscillation phenomenon in the discontinuous signal representation, thus reduces the reconstructed image quality. This paper proposed a new integer transform algorithm and its image compression method based on discontinuous orthogonal U-system. Firstly, the piecewise integration and the Gram-Schmidt process were used to calculate the two-dimensional orthogonal matrix of the U-system, and the scaling factors of row vectors were extracted to obtain the integer matrix. Secondly, the reversible integer U transform was established and the integer matrix was 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 was achieved by using matrix decomposition and sparse matrices. Finally, the integer U transform module and inverse transform module were 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 compression 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

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