基于小波变换的图像压缩方法研究

【作者】 周国瑞；

【导师】 张先迪；

【作者基本信息】 电子科技大学 ， 运筹学与控制论， 2003， 硕士

【摘要】 在小波变换图像压缩方法中，小波基选择的好坏，直接决定小波系数的性质，从而影响压缩过程中后继的其它处理，影响最终的压缩比和图像重建质量；小波变换的实现方法决定着计算的复杂度、数据的恢复性能等，从而影响压缩时间和图像重建质量。本文围绕小波变换图像压缩方法这一课题，对小波基的选取、小波变换的实现、小波系数的优化、自适应小波的构造、IWT的性能分析及优化实现进行了深入有价值的研究，所做的工作及创新成果有：(1) 概述了图像压缩的原理、压缩系统的结构及性能评价指标、图像压缩的发展现状。(2) 评述了从连续小波变换到R小波变换的去冗余过程、紧支撑双正交小波的构造、基于第一代小波的函数正交分解(Mallat算法)与双正交分解(推广的Mallat算法)、小波变换的时－频分析特性及多分辨分析特性在图像压缩中的应用。(3) 根据近些年发表的文章，分析并系统整理了第二代小波变换的理论与实现方法，分析了第二代小波变换的优势及这些优势在图像压缩中的应用。(4) 分析了图像小波变换后小波系数的特征，讨论了优化小波系数的小波基选择问题。(5) 提出了构造自适应小波变换以适应图像局部特征的思想，给出了两种自适应小波的构造方法，并分析了所构造小波在图像压缩中的性能。两种构造方法分别是：a) 构造自适应预测小波变换的方法。b) 构造自适应提升小波变换的方法。(6) 提出了在小波变换前加平滑预处理以削弱图像局部特征的思想，通过平滑预处理可优化小波系数，有效提高压缩比。(7) 对IWT的性能及产生原因进行了分析，真对其在有损压缩中劣于DWT的特点，提出了两种改进方案。a) 优化因式分解，以减少取整误差的引入。b) 扩幅，以效屏蔽取整误差。更多还原

【Abstract】 In the wavelet image compression system，the choice of wavelet basis directly determines the statistical characteristics of wavelet coefficients, thus it not only affects subsequent processes, but also affects the final compression ratio and the the quality of reconstructed image. The method of realizing wavelet transform determines computational complexity, whether the transformed data can be lossless recovered or not, etc., accordingly it can affect the time spending on compression and the quality of reconstructed image.In this paper, the author has performed comprehensive research on the method of wavelet basis selection, wavelet transform realization, wavelet coefficients’ optimization, adaptive wavelet’s construction, the performance analysis and optimal realization of IWT. The work and innovative results are as follows: 1.Have analyzed principles of image compression, the structure of compression system, methods of evaluating compression system’s performance and present methods of image compression. 2.Have summarized the process from continuous wavelet transform to R wavelet transform to gradually eliminate redundancy, the method of constructing biorthogonal and compactly supported wavelets, function’s decomposition based on orthogonal or biorthogonal basis, the time-frequency characterization of the first generation wavelet transform and the application of the multi-resolution characterization in image compression.3. Have analyzed and systemically summarized principles and realizing methods of the second generation wavelet, have analyzed advantages of the second generation wavelet transform and their applications in image compression.4.Have analyzed properties of wavelet coefficients obtained from an image through wavelet transform, and discussed how to select wavelet basis to optimize wavelet coefficients.5. Have put forward the idea of constructing adaptive wavelet transform to adapt to an image’s local characters, given two methods of constructing adaptive wavelet and analyzed the performance of adaptive wavelets in image compression. Two methods are:a) the method of constructing adaptive predict wavelet.<WP=6>b) the method of constructing adaptive update wavelet.6. Have put forward the idea of introducing smooth process before wavelet transform to weaken an image’s local characters. Experiments show the method can optimize wavelet coefficients and increase compression ratio.7. Have analyzed the performance of IWT and reasons resulting in the performance, and put forward two methods to improve its performance inferior to DWT in lossy compression. Two methods area) optimizing factorization to decrease the error of rounding operations.b) amplifying range to avoid the error of rounding operations.更多还原