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

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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.