Mathematical Sciences: Diffusion flows propagating with curature-dependent speed with applications to image processing

[405808]给出了依赖于均值函数、高斯函数和其他曲率函数随速度传播的非线性扩散流的连续研究。这种扩散过程在相变、火焰传播、材料磨损、信号和图像处理等模型中起着至关重要的作用。问题的存在，唯一性，奇点的开始，和渐近性质将被研究。将开发和测试用于计算扩散流的有效和健壮的算法。研究结果将用于改进现有的和开发新的图像和信号处理计算算法和代码。预计所开发的图像处理代码将在通信，医学，目标识别和全球变化研究中具有各种重要应用，特别是对于大气湍流扭曲的图像去噪。

9405808 Oliker A continuing investigation of nonlinear diffusion flows propagating with speed depending on mean, Gauss, and other curvature functions is proposed. Such diffusion processes play a critical role in models of phase transitions, flame propagation, material wearing, signal and image processing, and others. Questions of existence, uniqueness, onset of singularities, and asymptotic properties will be studied. Efficient and robust algorithms for computing diffusion flows will be developed and tested. The results will be applied to improve existing and develop new computational algorithms and codes for image and signal processing. It is anticipated that the developed image processing codes will have a variety of important applications in communications, medicine, target identification, and Global Change studies, especially for denoising images distorted by atmospheric turbulence.