New variational computational methods for modeling dual spaces of distributions, decomposition of functions, oscillations, and inverse problems in image analysis

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The investigators will study new computational techniques withapplications to inverse problems and image analysis. They will seek newmethods that combine variational arguments with ideas from computationalharmonic analysis and partial differential equations in order to overcomelimitations of existing methods. The research will have three objectives:propose new models for cartoon and texture separation in images by workingwith spaces of distributions; propose completely new techniques formultiscale hierarchical decomposition of images; propose efficientalgorithms for solving inverse problems.From the proposed research and educational program, computational mathematics, image processing, as well as more general areas of science andengineering will benefit. Applications include image analysis, medicalimaging, satellite imaging, material science, and terrain data analysis,surveillance and inverse problems.