A Predictive Algorithm Based On The Ito Stochastic Differential Equation And Its Application

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.