Numerical Methods for Separable Nonlinear Inverse Problems with Constraint and Low Rank
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In this age, there are many applications of inverse problems to lots of areas ranging from astronomy, geoscience and so on. For example, image reconstruction and deblurring require the use of methods to solve inverse problems. Since the problems are subject to many factors and noise, we can't simply apply general inversion methods. Furthermore in the problems of interest, the number of unknown variables is huge, and some may depend nonlinearly on the data, such that we must solve nonlinear problems. It is quite different and significantly more challenging to solve nonlinear problems than linear inverse problems, and we need to use more sophisticated methods to solve these kinds of problems.
General Audience Abstract
In various research areas, there are many required measurements which can't be observed due to physical and economical reasons. Instead, these unknown measurements can be recovered by known measurements. This phenomenon can be modeled and be solved by mathematics.
- Masters Theses