Hybrid Krylov Subspace Iterative Methods for Inverse Problems

授课人:James Nagy

机构:Pacific Institute for the Mathematical Sciences(PIMS)

关键词: Scientific;    Mathematics;    Applied Mathematics;   

加拿大|英语

【 摘 要 】

Inverse problems arise in many imaging applications, such as imagereconstruction (e.g., computed tomography), image deblurring, anddigital super-resolution. These inverse problems are very difficultto solve; in addition to being large scale, the underlyingmathematical model is often ill-posed, which means that noise andother errors in the measured data can be highly magnified in computedsolutions. Regularization methods are often used to overcome thisdifficulty. In this talk we describe hybrid Krylov subspace basedregularization approaches that combine matrix factorization methodswith iterative solvers. The methods are very efficient for large scaleimaging problems, and can also incorporate methods to automaticallyestimate regularization parameters. We also show how the approachescan be adapted to enforce sparsity and nonnegative constraints.We will use many imaging examples that arise in medicine and astronomyto illustrate the performance of the methods, and at the same timedemonstrate a new MATLAB software package that provides an easy to useinterface to their implementations.This is joint work with Silvia Gazzola (University of Bath) andPer Christian Hansen (Technical University of Denmark).

【 授权许可】

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