逆問題特論 - 情報理工学系研究科 - 東京大学授業カタログ

逆問題特論

Advanced Theory of Inverse Problems

Inverse problems are the problems to reconstruct the cause of a phenomenon from its resultant data by inversely tracing the law of causality.

In inverse problems, the important issues are the measurements of physical quantities that directly relate to an unknown cause and the algorithms that reconstruct the unknown parameters without losing the data qualities.

In this lecture, basic theories and algorithms, as well as measurement methods for inverse problems, are introduced with applications to noninvasive measurements, non-destructive inspection, physical exploration, user interfaces, and image/signal analysis.

MIMA Search

授業計画

Part I. Ill-posedness and design of inverse problems ・Definition of inverse problems ・Ill-posedness of inverse problems ・Design of inverse problems: choice of integral kernels illustrated with examples in susceptibility mapping, synthetic aperture radar, chirp radar, optical coherence tomography, and eddy current testing Part II. Fundamentals of linear inverse problems Part III. Methods for nonlinear inverse problems ・Direct methods for nonlinear inverse problems ・Projection onto convex sets for nonlinear inverse problems ・Reproducing kernels for inverse problems ・Wavelets for inverse problems ・Weighted integral methods ・Euler’s homogeneous equations for inverse problems

授業の方法

Lecture. The slide and the video of the lectures will be uploaded.

成績評価方法

Term paper plus a few short papers

履修上の注意

After class, review the lecture slides and your notes. For all attendee from various departments, the basics of linear inverse problems that may be taught in some undergraduate departments are summarized in Part II: Fundamentals of linear inverse problems.