Applications of frame theory to diffraction data
| 整理番号 | 2026a037 |
|---|---|
| 種別 | 若手・学生研究-短期研究員 |
| 研究計画題目 | Applications of frame theory to diffraction data |
| 研究代表者 | Navneet Redhu（Indian Institute of Technology Indore・Ph.D. course in Mathematics） |
| 研究実施期間 |
2026年5月5日(火) ～
2026年5月17日(日) |
| 研究分野のキーワード | Applied Harmonic Analysis, Frame Theory on LCA groups, Wavelets, Dynamical Sampling |
| 本研究で得られた成果の概要 | Motivated by the need to stably recover physical observables from incomplete, noisy Fourier diffraction data, this research extends generalized sampling to operator-valued reconstruction under measurement uncertainty. In collaborative research with Prof. Ryoko Tomiyasu (Kyushu University), we established necessary and sufficient conditions for the uniqueness of the reconstructed quantity $Lg$, developed a weighted least-squares formulation using diagonal standard-deviation matrices, and derived explicit matrix representations via Lagrange multipliers. Comparative discussions with classical sampling models were conducted, and test setups with B-spline and wavelet frames were prepared. As a new initiative expanding on frame-theoretic sampling, a joint manuscript is in preparation for peer-reviewed journal publication, with ongoing collaborative plans for numerical testing. |
| 組織委員(研究集会) 参加者(短期共同利用) |
富安 亮子（九州大学IMI・教授） |