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」
2019年11月6日 - 2019年11月7日
■会場：京都大学 総合研究15号館 201セミナー室
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
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.