线性系统理论在分析分形-小波变换编码误差中的应用

The Analysis of Image Coding Error of Fractal-Wavelet Transformation by Using Linear System Theory

本文利用线性系统理论对Ｄａｖｉｓ所采用的自子树量化（ＳＱＳ）分形小波变换图像编码算法进行了深入分析，并发现ＳＱＳ变换的吸引子与动力系统的稳定状态具有一致性．因此编码过程实际上就是对动力系统的参数进行编码．通过这种分析使我们了解到了尺度函数系数的量化误差是怎样影响解码图像的，从而可以更有效地控制解码误差，并且由此还可以更深刻地认识ＳＱＳ算法中直接存储尺度函数系数方案给编、解码带来的巨大好处．

In this paper,we analysed the Self-Quantization of Subtrees (SQS)in Fractal-Wavelet transform for image coding al- gorithm of Davis by using the linear System theory.we found that there is an equivalence of the attractor of a SQS transformation and the steady-state of a dynamical system . So, the encoding Process is done by encoding the parameters of this dynamical system According to this we can know how quantization errors for the scaling function coefficients will affect the decoded image,then we have coned over the final decoded error. Also,if we store the scaling function coefficients directly,we will get a result in a marked improvement in quality with respect to quantization for image compression.