【作者】 顾斌杰；

【导师】 卢鹏飞； 沈锦飞；

【作者基本信息】 江南大学 ， 检测技术与自动化装置， 2005， 硕士

【摘要】 伊藤随机微分方程是表征随机过程特点的重要数学模型,它的建立取决于随机过程漂移系数和扩散系数的确定。伊藤随机微分方程的解过程是马尔可夫过程。对伊藤随机微分方程白化变换和泰勒逼近,可得局部线性化马尔可夫链模型。该模型的预测误差序列是方差为预测周期的零均值白高斯序列,方差的这种性质为减小预测误差序列的方差,得到优良且稳定的预测数据压缩性能,提供了有效的途径。基于随机过程的概率密度函数的峰谷点,协同扩散过程的漂移系数,马尔可夫链“移向中心点”的性质以及状态转移值之间的关系,文献[15]提出了构造伊藤随机微分方程的马尔可夫链近似模型算法。仿真结果表明:不论序列是否为线性,也不论序列是否为高斯分布,该算法预测误差序列的方差不仅远小于Burg格型预测器而且近乎为常数。马尔可夫链近似模型算法的这些性质为其应用于图像压缩,得到相对稳定的压缩比提供了依据。仿真测试结果表明:马尔可夫链近似模型算法的压缩比、峰值信噪比和重建图像质量均优于JPEG基本系统的DCT编码,而且该算法的编解码时间比JPEG基本系统的DCT编码和EZW算法要短。最值得注意的是,该算法对于三幅标准图像的压缩比是高且相对稳定的。此外,如果EZW算法的初始阈值取得较大,则马尔可夫链近似模型算法重建图像的质量优于EZW算法。因此,马尔可夫链近似模型算法在图像压缩领域具有广阔的应用前景。更多还原

【Abstract】 The Ito stochastic differential equation is an important mathematical model for indicating thecharacteristic of the stochastic process. The construction of the Ito stochastic differential equationdepends on determining the drift coefficient and diffusion coefficient. The solution process of theIto stochastic differential equation is a Markov process. By using the whitening transformation andTaylor approximation, the Ito stochastic differential equation can be transformed into a locallylinearized Markov chain model. The prediction error series of the chain is a zero mean whiteGaussian series whose variance is equal to its prediction period. This property of the variance offersan effective way of reducing the variance of the prediction error series and acquiring excellent andstable performance of predictive data compression.Based on the relationship among the peak points and valley points of the probability densityfunction of stochastic process, the drift coefficient of its associated diffusion process, the ‘shift backto center’ property of the Markov chain and the state transitive value of the chain, an algorithm forconstructing the approximating model of the Markov chain (AMMC) algorithm of the Ito stochasticdifferential equation is put forward in the fifteenth reference. The results of simulation demonstratethat the variance of the prediction error series of the AMMC algorithm is not only far smaller thanthat of the Burg lattice predictor but also very close to constant whether the series is linear and itsdistribution is Gaussian distribution or not.These properties of the AMMC algorithm offer basis for it to be applied in the imagecompression and acquiring relatively stable compression ratio. The results of simulation testdemonstrate that the compression ratio, peak signal to noise ratio and the quality of thereconstructed image of the AMMC algorithm are all better than those of Discrete Cosine Transform(DCT) encoding of the JPEG basic system. Also the time of encoding and decoding of the AMMCalgorithm is shorter than that of the DCT encoding of the JPEG basic system and EmbeddedZerotree Wavelet (EZW) algorithm. Most important of all, the compression ratio of the AMMCalgorithm is relatively stable as to three standard images. Furthermore, if the initial threshold ofEZW algorithm is relatively big, the image reconstructed by the AMMC algorithm is better thanthat of EZW algorithm. Therefore, the AMMC algorithm opens up an attractive prospect for it to bewidely used in image compression.更多还原