【摘要】 针对图像处理的偏微分方程方法求解效率低的问题,提出了一种小波精细积分法,将小波数值方法和精细积分方法有机结合,利用小波数值方法的自适应性和精细积分方法与迭代步长无关的优良数值特性,有效提高了偏微分方程的计算速度。将该方法应用于基于热传导方程的图像去噪技术中,实验结果表明了该方法的正确性和有效性。更多还原

【Abstract】 The bottleneck of the image processing method based on the partial differential equations (PDEs) is the calculation efficiency. Aimed at this, a new numerical method on PDEs is proposed in this paper, which is called wavelet precise integration method(WPIM). This method combines the wavelet numerical method with the PIM, and so it possesses both the self-adaptability of the wavelet numerical method and the property that calculation precision independent to the time step which is the excellent merit of PIM. And so the WPIM improve the calculation efficiency of PDEs. And then this new method is used in image denoising technology based on the heat conduction equations. It shows that this method is correct and efficient.更多还原