A wavelet-based analysis of fractal image compression
A wavelet-based analysis of fractal image compression
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DOI：
10.1109/83.660992
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发表时间：
1998-02-01
影响因子：
10.6
通讯作者：
Davis, GM
中科院分区：
文献类型：
--
作者：
Davis, GM
为什么分形图像压缩会起作用？分形块编码背后的隐含图像模型是什么？我们如何描述哪种类型的图像可以很好地用于分形块编码器？这些是我们要解决的中心问题。我们提出了一种新的基于小波的分析基于块的分形压缩方案的框架。在这个框架内，我们能够借鉴成熟的变换编码器范例的见解。为了解决为什么分形块编码器工作的问题，我们证明了Jacquin[1]介绍的形式的分形块编码器是Haar小波子树量化方案，我们研究了具有附加消失矩的平滑小波的方案的推广。我们的通用编码器的性能可与文献中针对Jacquin样式编码方案的最佳结果相媲美。我们的小波框架使我们对分块编码器的收敛特性有了新的认识，并使我们发展了一种无条件收敛的方案和快速译码算法。我们用这个新算法进行的实验表明，分形编码器的有效性很大程度上来自于它们有效地表示小波零树的能力。最后，我们的框架揭示了当前分形压缩方案的一些基本限制。
Why does fractal image compression work? What is the implicit image model underlying fractal block coding? How can we characterize the types of images for which fractal block coders will work well? These are the central issues we address. We introduce a new wavelet-based framework for analyzing block-based fractal compression schemes. Within this framework we are able to draw upon insights from the well-established transform coder paradigm in order to address the issue of why fractal block coders work, We show that fractal block coders of the form introduced by Jacquin [1] are Haar wavelet subtree quantization schemes, We examine a generalization of the schemes to smooth wavelets with additional vanishing moments. The performance of our generalized coder is comparable to the best results in the literature for a Jacquin-style coding scheme. Our wavelet framework gives new insight into the convergence properties of fractal block coders, and it leads us to develop an unconditionally convergent scheme with a fast decoding algorithm. Our experiments with this new algorithm indicate that fractal coders derive much of their effectiveness from their ability to efficiently represent wavelet zerotrees. Finally, our framework reveals some of the fundamental limitations of current fractal compression schemes.