RIMS 共同研究（グループ型A）「多次元 Stockwell 変換と時間周波数解析」

■日時：2019年11月6日～7日

■会場：京都大学　総合研究15号館　201セミナー室

■研究会ウェブページ：http://www.osaka-kyoiku.ac.jp/~ashino/rims2019/

■プログラム：

11 月6日（水）

13:00 – 14:00 Luigi Riba (Data engineer and product specialist, Irion, Italy)

A link among multi-dimensional Stockwell transform, Gabor transform and wavelet transform

The reasoning behind the definition of the multi-dimensional Stockwell trans- form is described
in detail. Several continuous inversion formulas for the multi-dimensional Stockwell
transform under different sets of hypothesis are provided.

14:15 – 15:15 Tamotu Kinoshita (Mathematics, University of Tsukuba)

On directional frames having Lipschitz continuous Fourier transforms As a discretization of
two-dimensional wavelet transforms, we study direc- tional frames having Lipschitz
continuous Fourier transforms based on con- centric regular 2N -sided polygons in the
frequency domain. Especially, we consider a new simple way of expansions with non-Parseval
frames for better reconstructions. Moreover, we also propose a discretization scheme of
the inversion of the Radon transform, and represent the solution of the wave

equation.

15:45 – 16:45 Kazuaki Nakane (Internal Medicine, Osaka University)

Cytology support system via topological idea

Cytodiagnosis is a method for diagnosing whether cancer cells are contained in cells collected
from the human body. Because it can be performed eas- ily, the number of diagnoses
is increasing year by year. The shortage of pathologists is serious problem in
global, and the development of assistive technology using computers is an urgent issue. In
this talk, the method using

topological ideas and several results are introduced.

11 月 7 日（木）

9:30 – 10:30 Luigi Riba (Data engineer and product specialist, Irion, Italy)

Discrete orthonormal Stockwell transform and two-dimensional applica- tions

The discrete orthonormal Stockwell transform, its properties and its exten- sion to the
multi-dimensional case are described. An application of Stockwell transform to Ground Penetrating
Radar (GPR) images is given.

10:45 – 11:45 Shinya Moritoh (Mathematics, Nara Women’s University)

Two-microlocal estimates in wavelet theory and related function spaces We talk about
two-microlocal estimates in wavelet theory and related func- tion spaces, which is a
continuation of our work in 2004 and 2016. Some applications are also considered.

13:15 – 14:15 Kensuke Fujinoki (Mathematical Sciences, Tokai University)

Aspects of frame analysis

Frame theory has been known as a branch of functional analysis while a frame itself
has also been known as an indispensable tool used in a wide range of data analysis,
especially signal processing. In this talk we overview the basic and general theory for frame
analysis, and introduce the recent de- velopments and applications in signal processing including
sampling theory, Gabor systems and wavelet systems.

14:30 – 15:30 Zhong Zhang (Mechanical Engineering, Toyohashi University of Technology)

Cracks in Concrete Detected by 2 Dimensional Complex Discrete Wavelet Packet Transform using
complex-valued Haar wavelet

In this study, we focused on the ability to detect cracks, and designed a
complex-valued Haar wavelet, and applied it to 2D-CWPT. 2D-CWPT and anisotropic diffusion filter
were combined, and tested, and a crack detection method for linear cracks was proposed
through interpolation of the crack

loss area and extraction processing according to the shape feature.

http://www.osaka-kyoiku.ac.jp/~ashino/rims2019/rims2019program.pdf

■主催：京都大学　数理解析研究所

■協力：九州大学マス・フォア・インダストリ研究所
（文部科学省科学技術試験研究委託事業「数学アドバンストイノベーションプラットフォーム（AIMaP）」受託機関）

■企画番号：2019A012