Abstract:

Digital images are used to analyze objects in a variety of applications, such as star clusters in astronomy, molecules in biology, and tumors in medicine. Often post-processing must be done to the collected data; this may involve reconstructing, restoring or enhancing the image. Mathematically these processes are modeled as inverse problems. Inverse problems usually cannot be solved analytically, and thus computational approaches must be used. In imaging, these computational problems are very large, requiring development of efficient solvers. Another difficulty is that the problems are very sensitive to errors, such as noise, in the data. This difficulty is usually handled by a technique called regularization. In this talk we describe some inverse problems that arise in imaging applications, approaches to regularize them, and our recent contributions to the development of iterative solvers.