标题： 小波变换和扩散方程：应用于“卡西尼”飞船观测数据的处理 显示英文标题

标题： Wavelet transform and diffusion equations: applications to the processing of the "Cassini" spacecraft observations

摘要： 我们证明了如果用扩散微分方程的解来代替快速振荡函数的积分，那么利用复数Morlet小波进行连续变换就变得容易实现。 这种方法最重要的优势在于初始数据可以用任意节点数的非均匀样本表示。 我们将所提出的方法应用于从卡西尼号航天器获得的土星A环图像的处理。 此外，我们通过使用偏微分方程的小波变换得到了信号与谐波函数的局部相关系数。 显示英文摘要

摘要： We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of this approach is that the initial data can be represented by non-uniform sample of an arbitrary node number. We apply the proposed method to the processing of the image of the Saturn A-ring obtained from the Cassini spacecraft. Also we have got via the wavelet transform using PDE, the local correlation coefficient of the signal and the harmonic function.